Generalized hypergeometric function and Generating function

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Difference between Generalized hypergeometric function and Generating function

Generalized hypergeometric function vs. Generating function

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation. In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.

Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

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Chebyshev polynomials

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x).

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Coefficient

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression.

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Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

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Dilogarithm

In mathematics, the dilogarithm (or Spence's function), denoted as, is a particular case of the polylogarithm.

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Falling and rising factorials

In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial \begin (x)_n.

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Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

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Laguerre polynomials

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: xy + (1 - x)y' + ny.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Polylogarithm

In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function of order and argument.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n.

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Q-Pochhammer symbol

In the mathematical field of combinatorics, the q-Pochhammer symbol, also called the q-shifted factorial, is the product (a;q)_n.

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Radius of convergence

In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges.

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Rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

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