Question

Deriving the Normalization formula for Associated Legendre functions: Stage $1$ of $4$

score 1.4k · Answer 1 · 2026-03-27 01:45:57

1.4k

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Deriving the Normalization formula for Associated Legendre functions: Stage $1$ of $4$

Published on 27 Mar 2026 - 1:45

score 61 · Answer 2 · 2016-04-24 09:37:30

61

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Show that $\frac{z}{1-z} = \sum_{j=0}^∞ \frac{2^j}{1 + z^{-2^j}}$ when $z ∈ \mathbb{D}$

Published on 24 Apr 2016 - 9:37

score 270 · Answer 3 · 2016-04-24 12:16:37

270

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Hellinger integral properties - proof of equivalence for infinite product measures

Published on 24 Apr 2016 - 12:16

score 321 · Answer 4 · 2016-04-24 18:42:15

321

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Knowing the representation of $\frac{π^2}{\sin^2(πz)}$, deduce the Taylor series of $\frac{z^2}{\sin^2{z}}$

Published on 24 Apr 2016 - 18:42

score 172 · Answer 5 · 2026-03-31 17:02:29

172

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Sequence of non-independent coin tosses

Published on 31 Mar 2026 - 17:02

score 227 · Answer 6 · 2016-04-26 19:56:19

227

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Prove that $ζ(4)=π^4/90$ knowing that $\sin(πz) = πz \prod_{n=1}^∞ \left( 1 - \frac{z^2}{n^2} \right)$

Published on 26 Apr 2016 - 19:56

score 78 · Answer 7 · 2026-03-30 13:11:15

78

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Infinite Sets Proof

Published on 30 Mar 2026 - 13:11

score 177 · Answer 8 · 2016-04-29 12:33:45

177

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Infinite product include summation

Published on 29 Apr 2016 - 12:33

score 409 · Answer 9 · 2026-03-31 12:17:16

409

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Given two entire functions $f_1,f_2$ without common zeros, prove that one can find some entire functions $g_1,g_2$ such that $f_1g_1+f_2g_2=1$

Published on 31 Mar 2026 - 12:17

score 189 · Answer 10 · 2016-05-02 00:09:47

189

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Calculate $\sum_{n=1}^\infty \frac{1}{n^4}$.

Published on 02 May 2016 - 0:09

score 246 · Answer 11 · 2016-05-03 15:04:37

246

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Closed form for $\prod_{i=0}^{\infty}(1+x^{2^i})$

Published on 03 May 2016 - 15:04

score 76 · Answer 12 · 2016-05-03 18:30:55

Show that, $\prod_{k=2}^{\infty}\left(\prod_{n=0}^{\infty}(n!)^{\frac{k-1}{k^{n+1}}}\right)=\prod_{m=2}^{\infty}m^{\zeta(s)-1}$

score 69 · Answer 13 · 2016-05-03 21:55:10

69

Views

Can this Gamma function expression be reduce to its lowest form?

Published on 03 May 2016 - 21:55

score 178 · Answer 14 · 2016-05-08 09:37:12

178

Views

$\cos(\pi x) = \prod_{n=0}^{\infty} \left( 1-\frac{x^2}{(n+\frac{1}{2})^2}\right)$?

Published on 08 May 2016 - 9:37

score 145 · Answer 15 · 2016-05-08 15:11:27

145

Views

Showing that $\sigma=\prod_{n=1}^{\infty}(n!)^{\frac{1}{2^{n+1}}}$

Published on 08 May 2016 - 15:11

List Question

Deriving the Normalization formula for Associated Legendre functions: Stage $1$ of $4$

Show that $\frac{z}{1-z} = \sum_{j=0}^∞ \frac{2^j}{1 + z^{-2^j}}$ when $z ∈ \mathbb{D}$

Hellinger integral properties - proof of equivalence for infinite product measures

Knowing the representation of $\frac{π^2}{\sin^2(πz)}$, deduce the Taylor series of $\frac{z^2}{\sin^2{z}}$

Sequence of non-independent coin tosses

Prove that $ζ(4)=π^4/90$ knowing that $\sin(πz) = πz \prod_{n=1}^∞ \left( 1 - \frac{z^2}{n^2} \right)$

Infinite Sets Proof

Infinite product include summation

Given two entire functions $f_1,f_2$ without common zeros, prove that one can find some entire functions $g_1,g_2$ such that $f_1g_1+f_2g_2=1$

Calculate $\sum_{n=1}^\infty \frac{1}{n^4}$.

Closed form for $\prod_{i=0}^{\infty}(1+x^{2^i})$

Show that, $\prod_{k=2}^{\infty}\left(\prod_{n=0}^{\infty}(n!)^{\frac{k-1}{k^{n+1}}}\right)=\prod_{m=2}^{\infty}m^{\zeta(s)-1}$

Can this Gamma function expression be reduce to its lowest form?

$\cos(\pi x) = \prod_{n=0}^{\infty} \left( 1-\frac{x^2}{(n+\frac{1}{2})^2}\right)$?

Showing that $\sigma=\prod_{n=1}^{\infty}(n!)^{\frac{1}{2^{n+1}}}$

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