Question

What is known about $\sum_{n=0}^{\infty} x^{n^3} $.

score 98 · Answer 1 · 2015-11-08 21:48:25

98

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What is known about $\sum_{n=0}^{\infty} x^{n^3} $.

Published on 08 Nov 2015 - 21:48

score 1.4k · Answer 2 · 2026-03-26 19:02:55

1.4k

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Orthogonality of Laguerre polynomials from generating function

Published on 26 Mar 2026 - 19:02

score 42 · Answer 3 · 2015-11-13 11:35:07

42

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When $\frac{e^{-\lambda } \lambda ^x}{x!}$ over positive integers is invertible?

Published on 13 Nov 2015 - 11:35

score 242 · Answer 4 · 2015-11-14 18:50:09

242

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How to solve harmonic oscillator-like equation with $\theta$-function?

Published on 14 Nov 2015 - 18:50

score 131 · Answer 5 · 2026-04-06 10:41:56

131

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Fundamental solution of a shifted operator

Published on 06 Apr 2026 - 10:41

score 726 · Answer 6 · 2026-04-04 03:57:15

726

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Show $\int_{0}^{\infty} \frac{x^{-z}}{(1 + x)^{2}} ~ \mathrm{d}{x} = \frac{\pi z}{sin(\pi z)}$

Published on 04 Apr 2026 - 3:57

score 107 · Answer 7 · 2026-04-06 10:40:16

107

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Integration of hypergeometric functions?

Published on 06 Apr 2026 - 10:40

score 169 · Answer 8 · 2026-04-06 12:57:57

169

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Derivative of the quotient of 2 elliptic integrals of the first kind

Published on 06 Apr 2026 - 12:57

score 2.2k · Answer 9 · 2015-11-19 16:15:49

2.2k

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The trigonometric solution to the solvable DeMoivre quintic?

Published on 19 Nov 2015 - 16:15

score 146 · Answer 10 · 2015-11-19 22:51:07

146

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How to prove that only the sine waves keep their shape when they are added together and have the same period?

Published on 19 Nov 2015 - 22:51

score 491 · Answer 11 · 2026-04-05 20:13:54

491

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meijer g function explicit form

Published on 05 Apr 2026 - 20:13

score 2.8k · Answer 12 · 2015-11-23 12:29:41

2.8k

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Product of two hypergeometric functions

Published on 23 Nov 2015 - 12:29

score 857 · Answer 13 · 2026-03-31 07:52:36

857

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How do I develop numerical routines for the evaluation of my own special functions?

Published on 31 Mar 2026 - 7:52

score 204 · Answer 14 · 2026-03-26 19:02:55

204

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Relation between these expressions involving the Hypergeometric function and the Gegenbauer polynomials

Published on 26 Mar 2026 - 19:02

score 155 · Answer 15 · 2026-04-05 19:06:36

155

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Alternative definition of Gamma function. Show that $ \lim_{n \to \infty} \frac{n! \; n^m}{m \times (m+1) \times \dots \times (m+n)} = (m-1)!$

Published on 05 Apr 2026 - 19:06

List Question

What is known about $\sum_{n=0}^{\infty} x^{n^3} $.

Orthogonality of Laguerre polynomials from generating function

When $\frac{e^{-\lambda } \lambda ^x}{x!}$ over positive integers is invertible?

How to solve harmonic oscillator-like equation with $\theta$-function?

Fundamental solution of a shifted operator

Show $\int_{0}^{\infty} \frac{x^{-z}}{(1 + x)^{2}} ~ \mathrm{d}{x} = \frac{\pi z}{sin(\pi z)}$

Integration of hypergeometric functions?

Derivative of the quotient of 2 elliptic integrals of the first kind

The trigonometric solution to the solvable DeMoivre quintic?

How to prove that only the sine waves keep their shape when they are added together and have the same period?

meijer g function explicit form

Product of two hypergeometric functions

How do I develop numerical routines for the evaluation of my own special functions?

Relation between these expressions involving the Hypergeometric function and the Gegenbauer polynomials

Alternative definition of Gamma function. Show that $ \lim_{n \to \infty} \frac{n! \; n^m}{m \times (m+1) \times \dots \times (m+n)} = (m-1)!$

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