## Serie Drama-Serien

Die besten aktuellen Serien in den Seriencharts von batresponsibility.eu Der wöchentliche Überblick über das Ranking der erfolgreichen Serien. Die erfolgreichstens Serien in den Seriencharts von batresponsibility.eu Der Überblick über das Ranking der erfolgreichen Serien aus Deutschland, USA, UK. Was sind die besten Serien aller Zeiten? Entdecke auf batresponsibility.eu die besten Serien, wie zum Beispiel: Game Of Thrones, Breaking Bad. Serie (latein. serere „reihen“, „fügen“) bezeichnet: Fernsehserie, eine Abfolge von zusammenhängenden filmischen Werken im Fernsehen; Schriftenreihe, eine. Entdecke die besten Serien: Breaking Bad, Game of Thrones, Chernobyl, True Detective, Sherlock, The Wire, Die Sopranos, Rick and Morty, Rocket Beans TV. Hier findest du alle Serien, die aktuell bei Netflix, Amazon, Sky und Co. verfügbar sind ➤ Die neusten Trailer, Recaps und News zu deinen Lieblingsserien. Aktuelle News zu Fernsehserien.

Serie (latein. serere „reihen“, „fügen“) bezeichnet: Fernsehserie, eine Abfolge von zusammenhängenden filmischen Werken im Fernsehen; Schriftenreihe, eine. Die besten aktuellen Serien in den Seriencharts von batresponsibility.eu Der wöchentliche Überblick über das Ranking der erfolgreichen Serien. Du willst Serien online schauen? Deine liebsten Serien kostenlos sehen? Kein Problem: Alle aktuellen Serien im ZDF findest du in der Mediathek!## Serie Navigation menu Video

Caicedo scores on minute 98' to steal the victory! - Torino 3-4 Lazio - Top Moment - Serie A TIM## Serie Catch up with all the action - and watch free match highlights... Video

Gervinho Scores PERFECT first-time Volley! - Inter 2-2 Parma - Top Moment - Serie A TIM Anime Im Zentrum der Serie steht die U. Berührend Amelie Kiefer Horrorserie Der Held der Geschichte ist der im damaligen Britannien lebende Uht Suburra Suburra ist eine Mafiaserie, die mit dem einleitenden Leon Wessel-Masannek von Stefano Chilling Adventures Of Sabrina Gomorrah beginnt und mit Aswang Episoden als Serie fortgeführt wird.Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if the real part of s is greater than a number called the abscissa of convergence.

In many cases, a Dirichlet series can be extended to an analytic function outside the domain of convergence by analytic continuation.

This series can be directly generalized to general Dirichlet series. A series of functions in which the terms are trigonometric functions is called a trigonometric series :.

The most important example of a trigonometric series is the Fourier series of a function. Greek mathematician Archimedes produced the first known summation of an infinite series with a method that is still used in the area of calculus today.

Mathematicians from Kerala, India studied infinite series around CE. In the 17th century, James Gregory worked in the new decimal system on infinite series and published several Maclaurin series.

In , a general method for constructing the Taylor series for all functions for which they exist was provided by Brook Taylor. Leonhard Euler in the 18th century, developed the theory of hypergeometric series and q-series.

The investigation of the validity of infinite series is considered to begin with Gauss in the 19th century.

Euler had already considered the hypergeometric series. It established simpler criteria of convergence, and the questions of remainders and the range of convergence.

Cauchy insisted on strict tests of convergence; he showed that if two series are convergent their product is not necessarily so, and with him begins the discovery of effective criteria.

The terms convergence and divergence had been introduced long before by Gregory Leonhard Euler and Gauss had given various criteria, and Colin Maclaurin had anticipated some of Cauchy's discoveries.

Cauchy advanced the theory of power series by his expansion of a complex function in such a form. Abel in his memoir on the binomial series.

He showed the necessity of considering the subject of continuity in questions of convergence. Cauchy's methods led to special rather than general criteria, and the same may be said of Raabe , who made the first elaborate investigation of the subject, of De Morgan from , whose logarithmic test DuBois-Reymond and Pringsheim have shown to fail within a certain region; of Bertrand , Bonnet , Malmsten , , the latter without integration ; Stokes , Paucker , Chebyshev , and Arndt General criteria began with Kummer , and have been studied by Eisenstein , Weierstrass in his various contributions to the theory of functions, Dini , DuBois-Reymond , and many others.

Pringsheim's memoirs present the most complete general theory. The theory of uniform convergence was treated by Cauchy , his limitations being pointed out by Abel, but the first to attack it successfully were Seidel and Stokes — Cauchy took up the problem again , acknowledging Abel's criticism, and reaching the same conclusions which Stokes had already found.

Thomae used the doctrine , but there was great delay in recognizing the importance of distinguishing between uniform and non-uniform convergence, in spite of the demands of the theory of functions.

A series is said to be semi-convergent or conditionally convergent if it is convergent but not absolutely convergent.

Semi-convergent series were studied by Poisson , who also gave a general form for the remainder of the Maclaurin formula. The most important solution of the problem is due, however, to Jacobi , who attacked the question of the remainder from a different standpoint and reached a different formula.

This expression was also worked out, and another one given, by Malmsten Schlömilch Zeitschrift , Vol.

Genocchi has further contributed to the theory. Fourier series were being investigated as the result of physical considerations at the same time that Gauss, Abel, and Cauchy were working out the theory of infinite series.

Series for the expansion of sines and cosines, of multiple arcs in powers of the sine and cosine of the arc had been treated by Jacob Bernoulli and his brother Johann Bernoulli and still earlier by Vieta.

Euler had already given the formulas for determining the coefficients in the series; Fourier was the first to assert and attempt to prove the general theorem.

Poisson —23 also attacked the problem from a different standpoint. Fourier did not, however, settle the question of convergence of his series, a matter left for Cauchy to attempt and for Dirichlet to handle in a thoroughly scientific manner see convergence of Fourier series.

Dirichlet's treatment Crelle , , of trigonometric series was the subject of criticism and improvement by Riemann , Heine, Lipschitz , Schläfli , and du Bois-Reymond.

Among other prominent contributors to the theory of trigonometric and Fourier series were Dini , Hermite , Halphen , Krause, Byerly and Appell.

Asymptotic series , otherwise asymptotic expansions , are infinite series whose partial sums become good approximations in the limit of some point of the domain.

In general they do not converge, but they are useful as sequences of approximations, each of which provides a value close to the desired answer for a finite number of terms.

The difference is that an asymptotic series cannot be made to produce an answer as exact as desired, the way that convergent series can.

In fact, after a certain number of terms, a typical asymptotic series reaches its best approximation; if more terms are included, most such series will produce worse answers.

Under many circumstances, it is desirable to assign a limit to a series which fails to converge in the usual sense. A summability method is such an assignment of a limit to a subset of the set of divergent series which properly extends the classical notion of convergence.

A variety of general results concerning possible summability methods are known. The Silverman—Toeplitz theorem characterizes matrix summability methods , which are methods for summing a divergent series by applying an infinite matrix to the vector of coefficients.

The most general method for summing a divergent series is non-constructive, and concerns Banach limits. Definitions may be given for sums over an arbitrary index set I.

The notion of convergence needs to be strengthened, because the concept of conditional convergence depends on the ordering of the index set.

Thus, we obtain the common notation for a series indexed by the natural numbers. Any sum over non-negative reals can be understood as the integral of a non-negative function with respect to the counting measure , which accounts for the many similarities between the two constructions.

This need not be true in a general abelian topological group see examples below. By nature, the definition of unconditional summability is insensitive to the order of the summation.

Hence, in normed spaces, it is usually only ever necessary to consider series with countably many terms. Summable families play an important role in the theory of nuclear spaces.

The notion of series can be easily extended to the case of a seminormed space. More generally, convergence of series can be defined in any abelian Hausdorff topological group.

One may define by transfinite recursion :. MR From Wikipedia, the free encyclopedia. Infinite sum. This article is about infinite sums.

For finite sums, see Summation. Limits of functions Continuity. Mean value theorem Rolle's theorem. Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem.

Fractional Malliavin Stochastic Variations. Glossary of calculus. Glossary of calculus List of calculus topics. Main article: e mathematical constant.

Main article: Absolute convergence. Main article: Conditional convergence. Main article: Convergence tests. Main article: Function series.

Main article: Power series. Main article: Formal power series. Main article: Laurent series. Main article: Dirichlet series.

Main article: Trigonometric series. Main article: Divergent series. Actually, one usually assumes more: the family of functions is locally finite , that is, for every x there is a neighborhood of x in which all but a finite number of functions vanish.

This space is not separable. Calculus Made Easy. Math Vault. Retrieved Basic hypergeometric series. Cambridge university press. Alekseyev, On convergence of the Flint Hills series , arXiv Computing hypergeometric functions rigorously.

Functions of matrices: theory and computation. Society for industrial and applied mathematics. The scaling and squaring method for the matrix exponential revisited.

SIAM review, 51 4 , February University of St Andrews. School Science and Mathematics. General Topology: Chapters 1—4. Travel back in time to check out the early roles of some of Hollywood's heavy hitters.

Plus, see what some of your favorite '90s stars look like now. See the full gallery. Marine Sergeant Nicholas Brody is both a decorated hero and a serious threat.

CIA officer Carrie Mathison is tops in her field despite being bipolar. The delicate dance these two complex characters perform, built on lies, suspicion, and desire, is at the heart of this gripping, emotional thriller in which nothing short of the fate of our nation is at stake.

Written by ahmetkozan. From the beginning Homeland had always cutting edge drama. There has been many great seasons and I never thought it would continue as far as it went.

Season 8 however wasn't great, it should of wrapped in season 7. Overall though I enjoyed it, it is an intelligent and insightful show about modern day counter-terrorism and I hope they make a show as good in the future.

There has been several attempts but non reached the levels that Homeland did. Looking for some great streaming picks? Check out some of the IMDb editors' favorites movies and shows to round out your Watchlist.

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Rate This. Episode Guide. A bipolar CIA operative becomes convinced a prisoner of war has been turned by al-Qaeda and is planning to carry out a terrorist attack on American soil.

Creators: Alex Gansa , Howard Gordon. Available on Amazon. Added to Watchlist. Top-Rated Episodes S4. Error: please try again.

Stars of the s, Then and Now.

Full Cast and Crew. Metacritic Reviews. English Language Learners Definition of series. This expression was also worked out, and another one given, by Malmsten Keep scrolling for more. Dirichlet's treatment Crelle, of trigonometric series was the subject of criticism and improvement by RiemannHeine, LipschitzSchläfliand du Bois-Reymond. Southland Tales Fractional Malliavin Stochastic Variations.Series are classified not only by whether they converge or diverge, but also by the properties of the terms a n absolute or conditional convergence ; type of convergence of the series pointwise, uniform ; the class of the term a n whether it is a real number, arithmetic progression, trigonometric function ; etc.

When a n is a non-negative real number for every n , the sequence S N of partial sums is non-decreasing.

The exact value of the original series is the Basel problem. This is sufficient to guarantee not only that the original series converges to a limit, but also that any reordering of it converges to the same limit.

A series of real or complex numbers is said to be conditionally convergent or semi-convergent if it is convergent but not absolutely convergent.

A famous example is the alternating series. Abel's test is an important tool for handling semi-convergent series.

If a series has the form. This applies to the point-wise convergence of many trigonometric series, as in. The evaluation of truncation errors is an important procedure in numerical analysis especially validated numerics and computer-assisted proof.

Then the next inequality holds:. Taylor's theorem is a statement that includes the evaluation of the error term when the Taylor series is truncated.

By using the ratio , we can obtain the evaluation of the error term when the hypergeometric series is truncated.

There exist many tests that can be used to determine whether particular series converge or diverge. Equivalently, the partial sums.

A stronger notion of convergence of a series of functions is the uniform convergence. Uniform convergence is desirable for a series because many properties of the terms of the series are then retained by the limit.

For example, if a series of continuous functions converges uniformly, then the limit function is also continuous.

Tests for uniform convergence include the Weierstrass' M-test , Abel's uniform convergence test , Dini's test , and the Cauchy criterion. More sophisticated types of convergence of a series of functions can also be defined.

In measure theory , for instance, a series of functions converges almost everywhere if it converges pointwise except on a certain set of measure zero.

Other modes of convergence depend on a different metric space structure on the space of functions under consideration. The Taylor series at a point c of a function is a power series that, in many cases, converges to the function in a neighborhood of c.

For example, the series. The radius of this disc is known as the radius of convergence , and can in principle be determined from the asymptotics of the coefficients a n.

The convergence is uniform on closed and bounded that is, compact subsets of the interior of the disc of convergence: to wit, it is uniformly convergent on compact sets.

Historically, mathematicians such as Leonhard Euler operated liberally with infinite series, even if they were not convergent.

When calculus was put on a sound and correct foundation in the nineteenth century, rigorous proofs of the convergence of series were always required.

In this setting, the sequence of coefficients itself is of interest, rather than the convergence of the series. Formal power series are used in combinatorics to describe and study sequences that are otherwise difficult to handle, for example, using the method of generating functions.

In the most common setting, the terms come from a commutative ring , so that the formal power series can be added term-by-term and multiplied via the Cauchy product.

In this case the algebra of formal power series is the total algebra of the monoid of natural numbers over the underlying term ring. Laurent series generalize power series by admitting terms into the series with negative as well as positive exponents.

A Laurent series is thus any series of the form. If such a series converges, then in general it does so in an annulus rather than a disc, and possibly some boundary points.

The series converges uniformly on compact subsets of the interior of the annulus of convergence. A Dirichlet series is one of the form. For example, if all a n are equal to 1, then the Dirichlet series is the Riemann zeta function.

Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if the real part of s is greater than a number called the abscissa of convergence.

In many cases, a Dirichlet series can be extended to an analytic function outside the domain of convergence by analytic continuation.

This series can be directly generalized to general Dirichlet series. A series of functions in which the terms are trigonometric functions is called a trigonometric series :.

The most important example of a trigonometric series is the Fourier series of a function. Greek mathematician Archimedes produced the first known summation of an infinite series with a method that is still used in the area of calculus today.

Mathematicians from Kerala, India studied infinite series around CE. In the 17th century, James Gregory worked in the new decimal system on infinite series and published several Maclaurin series.

In , a general method for constructing the Taylor series for all functions for which they exist was provided by Brook Taylor.

Leonhard Euler in the 18th century, developed the theory of hypergeometric series and q-series. The investigation of the validity of infinite series is considered to begin with Gauss in the 19th century.

Euler had already considered the hypergeometric series. It established simpler criteria of convergence, and the questions of remainders and the range of convergence.

Cauchy insisted on strict tests of convergence; he showed that if two series are convergent their product is not necessarily so, and with him begins the discovery of effective criteria.

The terms convergence and divergence had been introduced long before by Gregory Leonhard Euler and Gauss had given various criteria, and Colin Maclaurin had anticipated some of Cauchy's discoveries.

Cauchy advanced the theory of power series by his expansion of a complex function in such a form. Abel in his memoir on the binomial series.

He showed the necessity of considering the subject of continuity in questions of convergence. Cauchy's methods led to special rather than general criteria, and the same may be said of Raabe , who made the first elaborate investigation of the subject, of De Morgan from , whose logarithmic test DuBois-Reymond and Pringsheim have shown to fail within a certain region; of Bertrand , Bonnet , Malmsten , , the latter without integration ; Stokes , Paucker , Chebyshev , and Arndt General criteria began with Kummer , and have been studied by Eisenstein , Weierstrass in his various contributions to the theory of functions, Dini , DuBois-Reymond , and many others.

Pringsheim's memoirs present the most complete general theory. The theory of uniform convergence was treated by Cauchy , his limitations being pointed out by Abel, but the first to attack it successfully were Seidel and Stokes — Cauchy took up the problem again , acknowledging Abel's criticism, and reaching the same conclusions which Stokes had already found.

Thomae used the doctrine , but there was great delay in recognizing the importance of distinguishing between uniform and non-uniform convergence, in spite of the demands of the theory of functions.

A series is said to be semi-convergent or conditionally convergent if it is convergent but not absolutely convergent.

Semi-convergent series were studied by Poisson , who also gave a general form for the remainder of the Maclaurin formula.

The most important solution of the problem is due, however, to Jacobi , who attacked the question of the remainder from a different standpoint and reached a different formula.

This expression was also worked out, and another one given, by Malmsten Schlömilch Zeitschrift , Vol. Genocchi has further contributed to the theory.

Fourier series were being investigated as the result of physical considerations at the same time that Gauss, Abel, and Cauchy were working out the theory of infinite series.

Series for the expansion of sines and cosines, of multiple arcs in powers of the sine and cosine of the arc had been treated by Jacob Bernoulli and his brother Johann Bernoulli and still earlier by Vieta.

Euler had already given the formulas for determining the coefficients in the series; Fourier was the first to assert and attempt to prove the general theorem.

Poisson —23 also attacked the problem from a different standpoint. Fourier did not, however, settle the question of convergence of his series, a matter left for Cauchy to attempt and for Dirichlet to handle in a thoroughly scientific manner see convergence of Fourier series.

Dirichlet's treatment Crelle , , of trigonometric series was the subject of criticism and improvement by Riemann , Heine, Lipschitz , Schläfli , and du Bois-Reymond.

Among other prominent contributors to the theory of trigonometric and Fourier series were Dini , Hermite , Halphen , Krause, Byerly and Appell.

Asymptotic series , otherwise asymptotic expansions , are infinite series whose partial sums become good approximations in the limit of some point of the domain.

In general they do not converge, but they are useful as sequences of approximations, each of which provides a value close to the desired answer for a finite number of terms.

The difference is that an asymptotic series cannot be made to produce an answer as exact as desired, the way that convergent series can.

In fact, after a certain number of terms, a typical asymptotic series reaches its best approximation; if more terms are included, most such series will produce worse answers.

Under many circumstances, it is desirable to assign a limit to a series which fails to converge in the usual sense.

A summability method is such an assignment of a limit to a subset of the set of divergent series which properly extends the classical notion of convergence.

A variety of general results concerning possible summability methods are known. The Silverman—Toeplitz theorem characterizes matrix summability methods , which are methods for summing a divergent series by applying an infinite matrix to the vector of coefficients.

The most general method for summing a divergent series is non-constructive, and concerns Banach limits. Definitions may be given for sums over an arbitrary index set I.

The notion of convergence needs to be strengthened, because the concept of conditional convergence depends on the ordering of the index set. Thus, we obtain the common notation for a series indexed by the natural numbers.

Any sum over non-negative reals can be understood as the integral of a non-negative function with respect to the counting measure , which accounts for the many similarities between the two constructions.

This need not be true in a general abelian topological group see examples below. By nature, the definition of unconditional summability is insensitive to the order of the summation.

Hence, in normed spaces, it is usually only ever necessary to consider series with countably many terms. Summable families play an important role in the theory of nuclear spaces.

The notion of series can be easily extended to the case of a seminormed space. More generally, convergence of series can be defined in any abelian Hausdorff topological group.

One may define by transfinite recursion :. MR Plot Keywords. Parents Guide. External Sites. User Reviews. User Ratings.

External Reviews. Metacritic Reviews. Photo Gallery. Trailers and Videos. Crazy Credits. Alternate Versions. Rate This. Episode Guide.

A bipolar CIA operative becomes convinced a prisoner of war has been turned by al-Qaeda and is planning to carry out a terrorist attack on American soil.

Creators: Alex Gansa , Howard Gordon. Available on Amazon. Added to Watchlist. Top-Rated Episodes S4. Error: please try again.

Stars of the s, Then and Now. Everything Coming to Hulu in October Top TV Shows of Emmys Trending Titles. TV Series to Watch. Series and movies to watch later.

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Episodes Seasons. Won 5 Golden Globes. Edit Cast Series cast summary: Claire Danes Carrie Mathison 96 episodes, Mandy Patinkin Saul Berenson 96 episodes, Rupert Friend Peter Quinn 58 episodes, Maury Sterling Max Piotrowski 45 episodes, F.

Murray Abraham Taglines: The nation sees a hero. She sees a threat.. Edit Did You Know? Trivia Halle Berry was originally offered the role of Carrie.

Kyle Chandler , Ryan Phillippe and Alessandro Nivola were also sought for the role of Brody but passed on the offer as they weren't interested in playing a villain.

Goofs In addition to showing Pakistani characters speaking Arabic, the names of the Arabs are incorrect. For example, Afzal is supposedly a Syrian terrorist, however a Syrian would be called Afdal, as the letter Dad is pronounced a hard d in Arabic while pronounced a Z in Farsi languages.

Same applies to Raqim, you would never find a Saudi of the name Raqim.

Ich denke, dass es die ausgezeichnete Idee ist.

Ich meine, dass Sie den Fehler zulassen. Schreiben Sie mir in PM.

man kann das Leerzeichen schlieГџen?