# Questions tagged [hypergeometric-functions]

Hypergeometric functions are the analytic functions defined by Taylor expansions of the shape $\sum_{n \geq 0} a_n x^n$, where $a_{n+1}/a_n$ is a rational function of $n$. This general family of functions encompasses many classical functions. The hypergeometric functions play an important role in many parts of mathematics.

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### Asymptotic expansion of hypergeometric function near $z=1$

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### Perform a univariate integral, involving a Gauss hypergeometric function

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### Compute the two-fold partial integral, where the three-fold full integral is known

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### What partial sum formulae exist for this basic hypergeometric series?

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### Correction terms in the asymptotic expansion of hypergeometric function

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### On the convergence of MIller's Algorithm for special function evaluation (hypergeometric 1F1)

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### Asymptotic expansion of an integral involving hypergeometric function

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### Euclidean volumes under the matrix norm of one-parameter subsets of unit balls of $2 \times 2$ matrices

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### A two argument sepcial function related to Legendre polynomial and Meixner polynomial

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### Conjectural nonvanishing of some combinatorial sums (6j symbols)

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### best-possible inequalities for hypergeometric functions

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### Integration of hypergeometric product for legendre polynomials

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### lower bound for absolute value of a hypergeometric function

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### Uniform Asymptotic Approximation of the Whittaker function

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### Limit of a hypergeometric function(1F2)

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### Understanding the branch cut and discontinuity of the hypergeometric function

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### Value of the hypergeometric function

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### A minimizing problem involving Gauss hypergeometric functions

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### How to use this generalised 'generating function' for the Gegenbauer polynomials

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### Compute Confluent Hypergeometric Function 1F1

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### Polya urn: Mean number of draws to get a specific sequence of colors?

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### integral involving hypergeometric function of matrix argument

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### Basis for solutions hypergeometric differential equation

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### Does the Riemann characterization of the hypergeometric function have a q-analog?

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### Is there a name for the hypergeometric function with more parameters than Lauricella but more variables than Kampé de Fériet?

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### Generalized hypergeometric function at $z=1$

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### Asymptotic behavior

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### Efficient numeric routines for computing $_2F_0$

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### What is the name of this special function?

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### Characterization of the hypergeometric function

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### Multivalued functions with three independent branches

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### Perform an integration involving the product of two hypergeometric functions

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### Generalized Lauricella functions?

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### Perform an integration over the unit interval of a two-parameter expression involving a Gauss hypergeometric function

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### Linear relation between $_3F_2$ at $z=1$

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### Integral involving Laguerre, Gaussian and modified Bessel function

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### Relation between elliptic curves and hypergeometric functions

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### Double Series involving Gamma function

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### Proving a particular “Abel type” identiy

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### Identity with binomial coefficients and k^k

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### Integral with Bessel function and hypergeometric function ${}_2F_2$: explicit expression for these polynomials?

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### Legendre functions as Hypergeometric functions

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### Closed form for $\int_0^T e^{-x}\frac{I_n(\alpha x)}{x}dx$

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### How to calculate the Lauricella function of type A by using matlab?

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### Solving a partial difference equation with variable coefficients explicitly

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### On the Integration and Manipulation of Expressions Involving Hypergeometric Functions

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### On modified Bessel solutions to complex ODE's using Kummer's series

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### Is a basic hypergeometric function ${}_2\phi_1(a, b; c; q, z)$ a meromorphic function in $z$?

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### Relation between different basis of solutions of an ODE

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