Question

How does $\zeta(1 - s)$ become $(-1/s + \cdots)$?

score 267 · Answer 1 · 2026-04-12 06:26:30

267

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How does $\zeta(1 - s)$ become $(-1/s + \cdots)$?

Published on 12 Apr 2026 - 6:26

score 526 · Answer 2 · 2026-04-15 22:17:06

526

Views

Hurwitz zeta function

Published on 15 Apr 2026 - 22:17

score 3.1k · Answer 3 · 2026-04-17 11:59:11

3.1k

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Proving a property of Legendre polynomials containing its derivatives: $nP_n(x)=x{P_n^\prime(x)} - P^\prime_{n-1}(x)$

Published on 17 Apr 2026 - 11:59

score 2.6k · Answer 4 · 2026-04-17 03:40:11

2.6k

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Problems regarding integrals involving Legendre polynomials: $\int_{-1}^1 x^2 P_{n-1}(x)P_{n+1}(x)dx = \frac{2n(n+1)}{(2n-1)(2n+1)(2n+3)}$

Published on 17 Apr 2026 - 3:40

score 270 · Answer 5 · 2026-04-15 16:15:12

270

Views

Solving for $x$ in $y=x^x(\ln x + 1)$ (Lambert W?)

Published on 15 Apr 2026 - 16:15

score 190 · Answer 6 · 2026-04-13 06:20:19

190

Views

Two $\psi$ functions

Published on 13 Apr 2026 - 6:20

score 381 · Answer 7 · 2026-04-14 13:31:07

381

Views

An injective map where each value is mapped to many others?

Published on 14 Apr 2026 - 13:31

score 78 · Answer 8 · 2026-04-17 09:57:49

78

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Find $\lim_{x\to \infty} \ln(\exp(\operatorname{LmW}(x))+1)(\exp(\operatorname{LmW}(x))+1) - x - \ln(x)$

Published on 17 Apr 2026 - 9:57

score 291 · Answer 9 · 2026-04-16 12:12:05

291

Views

To find closed form of $f(x)=\int_0^{\frac{\pi}{2}} e^{\sqrt{1-x^2 \sin^2 t}}\, dt$ as known functions

Published on 16 Apr 2026 - 12:12

score 366 · Answer 10 · 2026-04-17 05:12:13

366

Views

Limit of a summation wth Gamma function

Published on 17 Apr 2026 - 5:12

score 207 · Answer 11 · 2026-04-15 18:20:34

207

Views

Has the $\Gamma$-like function $f_p(n) = 1^{\ln(1)^p} \cdot 2^{\ln(2)^p} \cdot \ldots \cdot n^{\ln(n)^p} $ been discussed anywhere?

Published on 15 Apr 2026 - 18:20

score 77 · Answer 12 · 2026-04-14 07:27:56

77

Views

How to find $\lim_{x \rightarrow -N} J_{a} = (-1)^N J_{N}$?

Published on 14 Apr 2026 - 7:27

score 218 · Answer 13 · 2026-04-15 18:30:07

218

Views

How can I get $B(x,y+1)= \frac{y}{x+y} B(x,y)$ using integration by parts?

Published on 15 Apr 2026 - 18:30

score 487 · Answer 14 · 2026-04-12 00:29:41

487

Views

How to prove Gegenbauer's addition theorem?

Published on 12 Apr 2026 - 0:29

score 98 · Answer 15 · 2026-04-13 11:59:56

98

Views

for what $\nu$ does Riemann-Liouville differintegral of digamma function $\psi(z)$ exist?

Published on 13 Apr 2026 - 11:59

List Question

How does $\zeta(1 - s)$ become $(-1/s + \cdots)$?

Hurwitz zeta function

Proving a property of Legendre polynomials containing its derivatives: $nP_n(x)=x{P_n^\prime(x)} - P^\prime_{n-1}(x)$

Problems regarding integrals involving Legendre polynomials: $\int_{-1}^1 x^2 P_{n-1}(x)P_{n+1}(x)dx = \frac{2n(n+1)}{(2n-1)(2n+1)(2n+3)}$

Solving for $x$ in $y=x^x(\ln x + 1)$ (Lambert W?)

Two $\psi$ functions

An injective map where each value is mapped to many others?

Find $\lim_{x\to \infty} \ln(\exp(\operatorname{LmW}(x))+1)(\exp(\operatorname{LmW}(x))+1) - x - \ln(x)$

To find closed form of $f(x)=\int_0^{\frac{\pi}{2}} e^{\sqrt{1-x^2 \sin^2 t}}\, dt$ as known functions

Limit of a summation wth Gamma function

Has the $\Gamma$-like function $f_p(n) = 1^{\ln(1)^p} \cdot 2^{\ln(2)^p} \cdot \ldots \cdot n^{\ln(n)^p} $ been discussed anywhere?

How to find $\lim_{x \rightarrow -N} J_{a} = (-1)^N J_{N}$?

How can I get $B(x,y+1)= \frac{y}{x+y} B(x,y)$ using integration by parts?

How to prove Gegenbauer's addition theorem?

for what $\nu$ does Riemann-Liouville differintegral of digamma function $\psi(z)$ exist?

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