Question

The closed form of $\lim_{x\to\frac{4}{3}}\frac{\partial}{\partial x}\left[\,_2{\rm{F}}_1\left(\frac{1}{3},1;x;-1\right)\right]$

score 1.9k · Answer 1 · 2014-09-14 10:22:04

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The closed form of $\lim_{x\to\frac{4}{3}}\frac{\partial}{\partial x}\left[\,_2{\rm{F}}_1\left(\frac{1}{3},1;x;-1\right)\right]$

Published on 14 Sep 2014 - 10:22

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score 1.2k · Answer 7 · 2014-10-06 23:20:09

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Prove ${_2F_1}\left({{\tfrac16,\tfrac23}\atop{\tfrac56}}\middle|\,\frac{80}{81}\right)=\frac 35 \cdot 5^{1/6} \cdot 3^{2/3}$

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score 251 · Answer 8 · 2014-10-08 15:06:04

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score 458 · Answer 11 · 2014-10-18 08:30:51

458

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Closed-form of the sequence ${_2F_1}\left(\begin{array}c\tfrac12,-n\\\tfrac32\end{array}\middle|\,\frac{1}{2}\right)$

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score 291 · Answer 12 · 2014-10-19 22:48:36

291

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score 146 · Answer 13 · 2014-10-21 02:02:05

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1.4k

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score 604 · Answer 15 · 2014-10-27 23:41:47

604

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Prove this closed-form of sum of ${_4F_3}$ hypergeometric functions

Published on 27 Oct 2014 - 23:41

List Question

The closed form of $\lim_{x\to\frac{4}{3}}\frac{\partial}{\partial x}\left[\,_2{\rm{F}}_1\left(\frac{1}{3},1;x;-1\right)\right]$

Moment Generating Function of a Beta random variable.

Show that this Markov chain is recurrent

Integral versus hypergeometric series: how to solve this?

Expression of the Runge function's derivative

What is the closed form of a certain sum

Prove ${_2F_1}\left({{\tfrac16,\tfrac23}\atop{\tfrac56}}\middle|\,\frac{80}{81}\right)=\frac 35 \cdot 5^{1/6} \cdot 3^{2/3}$

A Sine integral: problem I

Integral of a function which yields a hyper-geometric function

Multiplying the results of a hypergeometric distribution to get a total probability

Closed-form of the sequence ${_2F_1}\left(\begin{array}c\tfrac12,-n\\\tfrac32\end{array}\middle|\,\frac{1}{2}\right)$

Evaluating a series of hypergeometric functions

What more can i do to this infinite sum?

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

Prove this closed-form of sum of ${_4F_3}$ hypergeometric functions

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