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convergence of series involving Appell function

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#integration #sequences-and-series #hypergeometric-function
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To obtain a closed form for the series related to special functions.

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#power-series #special-functions #closed-form #hypergeometric-function #pochhammer-symbol
43
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Linear relation between ${_2 F_1} (a,b,c,z)$ and ${_2 F_1} (a \pm 1,b \pm 1,c \pm 2,z)$

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#ordinary-differential-equations #recurrence-relations #hypergeometric-function
481
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Asymptotic value of Meijer G-function

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#asymptotics #residue-calculus #hypergeometric-function
94
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Expressing Kummer U function as Meijer G

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#special-functions #hypergeometric-function
276
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Analytic continuation for special case of Appell's $F_2$ hypergeometric function

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#special-functions #hypergeometric-function #analytic-continuation
108
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Special function related to a nonlinear ODE

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#ordinary-differential-equations #special-functions #hypergeometric-function #frobenius-method
139
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Closed form for $\sum_{k=0}^\infty \frac{x^{2 k+1}}{(2k+1) \Gamma (\frac{2k+1}{q})}$

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#sequences-and-series #gamma-function #hypergeometric-function
57
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Expression of a hypergeometric sum

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#combinatorics #summation #computational-mathematics #hypergeometric-function
243
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Second Kummer Function

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#complex-analysis #hypergeometric-function #wronskian
65
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Fast Pochhammer

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#calculus #hypergeometric-function
1k
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Integral involving hypergeometric function $\int_0^1[{}_2F_1(\frac13,\frac23;1;x^3)]^2dx$

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#integration #definite-integrals #special-functions #hypergeometric-function #modular-forms
98
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Accurate evaluation of ${}_2F_1(-n, 1-x; 2; 2)$

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#hypergeometric-function
187
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Derivative of generalized hypergeometric function

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#derivatives #hypergeometric-function
1.5k
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Hypergeometric function at $z=1$

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#real-analysis #ordinary-differential-equations #asymptotics #special-functions #hypergeometric-function

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