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Closed formed expression of an integral involving product of two hypergeometric function

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#integration #definite-integrals #special-functions #closed-form #hypergeometric-function
115
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Hypergeometric Function near z = 1

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#asymptotics #power-series #hypergeometric-function
64
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Solving a Lamé differential equation with a parameter out of boundaries.

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#complex-analysis #ordinary-differential-equations #hypergeometric-function #homogeneous-equation
126
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Evaluate the indefinite integral $\int\left(1-\left(1-x^{\frac{1}{a}}\right)^a\right)\mathrm dx\,$

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#calculus #integration #indefinite-integrals #hypergeometric-function #beta-function
55
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Relationship between ${}_3F_2$ hypergeometric functions

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#complex-analysis #power-series #hypergeometric-function
103
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Generalization of Gauss multiplication formula for $\Gamma(jm+kn+a);j,k\in\Bbb N$?

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#closed-form #gamma-function #transformation #hypergeometric-function #pochhammer-symbol
85
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Simplifying a sum of binomials, is there a closed form?

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#combinatorics #polynomials #binomial-coefficients #hypergeometric-function
85
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Hypergeometric Quadratic Transformations

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#integration #improper-integrals #hypergeometric-function
233
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Closed form of $\frac1s\int_0^\infty e^{-s(\tanh(t)+at)}dt=\frac1s\int_0^1e^{-st}(1-t)^{\frac{as}2-1}(1+t)^{-\frac{as}2-1}dt$ to invert $\tanh(x)+ax$?

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#laplace-transform #closed-form #hypergeometric-function #hyperbolic-functions #inverse-laplace
95
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Probability of getting the same pair of cards over 200 days of tarot readings?

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#probability #sequences-and-series #hypergeometric-function
27
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Hypergeometric function of the matrix argument $ _0F_1(b, cI_p)$ when the matrix is (proportional to) the identity

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#hypergeometric-function
122
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Series related to $\,_{2p+1}F_{2p}\left(\left\{\frac{a}{2}\right\}_{2p-1},a,\frac12;a+\frac{1}{2},\left\{1+\frac{a}{2}\right\}_{2p-1};1\right)$

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#real-analysis #calculus #contour-integration #hypergeometric-function #elliptic-integrals
23
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Finding a relationship between series coefficients in a system of integral equations: A challenge in solving the resulting linear system

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#calculus #sequences-and-series #taylor-expansion #power-series #hypergeometric-function
103
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How does a software (e.g., MATLAB) compute the value of a hypergeometric series that converges?

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#convergence-divergence #hypergeometric-function
95
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Evaluate $\sum_{n=0}^{\infty} \frac{(a)_n (b)_n}{(2b)_n} \frac{\psi^{(0)}\left (n+ \frac{a}2+1 \right ) }{\Gamma\left (n+ \frac{a}2+1 \right ) }$

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#real-analysis #sequences-and-series #closed-form #gamma-function #hypergeometric-function

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