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If $a,b,c$ are positive integers with $c\leq a+b,$ can I conclude that $_2F_1(a,b;c;1)$ diverges?

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#power-series #special-functions #gamma-function #hypergeometric-function
862
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Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

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#real-analysis #sequences-and-series #special-functions #hypergeometric-function
111
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multiplying a hypergeometric series

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#sequences-and-series #functions #hypergeometric-function
42
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Simplifying specific $\,_4F_3$ hypergeometric function?

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#hypergeometric-function
954
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How to calculate the Kampé de Fériet function?

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#sequences-and-series #discrete-mathematics #special-functions #gamma-function #hypergeometric-function
350
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A connection between the confluent hypergeometric function and Bessel functions.

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#ordinary-differential-equations #special-functions #hypergeometric-function
67
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How to get a formula for the definite integral mentioned below

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#integration #definite-integrals #complex-integration #hypergeometric-function
90
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Closed form for $c_m = \sum_{n=|m|}^{\infty} \left(\dfrac{1}{2}\right)^{2n} (-1)^{m+n}{2n \choose m+n}$, $m$ integer

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#sequences-and-series #combinatorics #fourier-series #hypergeometric-function
424
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The convergence and reality of Gauss Hypergeometric Function

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#complex-analysis #hypergeometric-function
134
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Tricomi confluent hypergeometric function

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#special-functions #hypergeometric-function
173
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an approximation to the generalized hypergeometric function

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#matlab #hypergeometric-function #approximation-theory #article-writing
167
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Integral of squared Hypergeometric Function

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#integration #definite-integrals #hypergeometric-function
186
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Solve the equation similar to the Kummer equation

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#ordinary-differential-equations #hypergeometric-function
134
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hypergeometric function with special Pochhammer symbol

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#hypergeometric-function
108
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What is this generalization of the Chebyshev polynomials?

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#special-functions #hypergeometric-function #orthogonal-polynomials #chebyshev-polynomials

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