Question

Integrating $\int_{1}^{\alpha} x^n(x^2-1)^{q-\frac{1}{2}}dx$

score 71 · Answer 1 · 2026-04-17 06:55:17

71

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Integrating $\int_{1}^{\alpha} x^n(x^2-1)^{q-\frac{1}{2}}dx$

Published on 17 Apr 2026 - 6:55

score 97 · Answer 2 · 2026-04-14 06:41:21

97

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Asymptotic behavior of the integral $\int_{0}^{\infty} e^{-\rho \cosh(R)}\cosh(Rq)dR$

Published on 14 Apr 2026 - 6:41

score 118 · Answer 3 · 2026-04-15 07:26:41

118

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Behavior of modified Bessel function $K_n(\rho)$ near zero

Published on 15 Apr 2026 - 7:26

score 54 · Answer 4 · 2026-04-17 10:22:11

Proving $-\text{Li}_2(x^{-1}-1)+\text{Li}_2(1-x^{-1})-\text{Li}_2(2 x)+\text{Li}_2(2-2 x)+\text{Li}_2(2) = i \pi \log(x)$ for $x>1/2$.

score 73 · Answer 5 · 2026-04-15 21:16:13

73

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Finite Integral involving modified Bessel Function, $\cos(2^n x)$, and exponential function

Published on 15 Apr 2026 - 21:16

score 141 · Answer 6 · 2026-04-15 07:03:01

141

Views

How to prove that $\int_{0}^{\infty} \frac{1}{\operatorname{Ai}(x)^{2}+\operatorname{Bi}(x)^{2}} dx = \frac{\pi^{2} }{6} $?

Published on 15 Apr 2026 - 7:03

score 160 · Answer 7 · 2026-04-13 18:00:37

160

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Monotonicity of a ratio of Gamma functions

Published on 13 Apr 2026 - 18:00

score 61 · Answer 8 · 2026-04-14 12:53:31

61

Views

I have to proof that the integral converge for all p >0

Published on 14 Apr 2026 - 12:53

score 49 · Answer 9 · 2026-04-11 02:30:57

49

Views

How to solve such complicated integral to get closed form expression.

Published on 11 Apr 2026 - 2:30

score 132 · Answer 10 · 2026-04-11 06:47:31

132

Views

Modified Bessel function integral representation for $n$ integer

Published on 11 Apr 2026 - 6:47

score 126 · Answer 11 · 2026-04-16 15:37:29

126

Views

Neat function $I(x,y)= \sum\limits_{n=1}^{\infty}\bigg|\int_0^1 \frac{1}{t~(\log t)^y}\exp\bigg(\frac{n^x}{\log t}\bigg) ~dt~\bigg| $. Closed form?

Published on 16 Apr 2026 - 15:37

score 251 · Answer 12 · 2026-04-09 01:31:21

251

Views

How to analytically continue a function across a branch cut

Published on 09 Apr 2026 - 1:31

score 96 · Answer 13 · 2026-04-17 01:41:36

96

Views

The Mellin transform as a mapping from a Hardy space to a weighted space

Published on 17 Apr 2026 - 1:41

score 79 · Answer 14 · 2026-04-14 02:39:20

79

Views

Combinatorial problem: triple binomial product related to squared Laguerre polynomials

Published on 14 Apr 2026 - 2:39

score 83 · Answer 15 · 2026-04-17 11:55:05

83

Views

Does any Hyper-geometric function can be analytically continuated to the whole complex plain except $e^{\pm i\pi/3}$

Published on 17 Apr 2026 - 11:55

List Question

Integrating $\int_{1}^{\alpha} x^n(x^2-1)^{q-\frac{1}{2}}dx$

Asymptotic behavior of the integral $\int_{0}^{\infty} e^{-\rho \cosh(R)}\cosh(Rq)dR$

Behavior of modified Bessel function $K_n(\rho)$ near zero

Proving $-\text{Li}_2(x^{-1}-1)+\text{Li}_2(1-x^{-1})-\text{Li}_2(2 x)+\text{Li}_2(2-2 x)+\text{Li}_2(2) = i \pi \log(x)$ for $x>1/2$.

Finite Integral involving modified Bessel Function, $\cos(2^n x)$, and exponential function

How to prove that $\int_{0}^{\infty} \frac{1}{\operatorname{Ai}(x)^{2}+\operatorname{Bi}(x)^{2}} dx = \frac{\pi^{2} }{6} $?

Monotonicity of a ratio of Gamma functions

I have to proof that the integral converge for all p >0

How to solve such complicated integral to get closed form expression.

Modified Bessel function integral representation for $n$ integer

Neat function $I(x,y)= \sum\limits_{n=1}^{\infty}\bigg|\int_0^1 \frac{1}{t~(\log t)^y}\exp\bigg(\frac{n^x}{\log t}\bigg) ~dt~\bigg| $. Closed form?

How to analytically continue a function across a branch cut

The Mellin transform as a mapping from a Hardy space to a weighted space

Combinatorial problem: triple binomial product related to squared Laguerre polynomials

Does any Hyper-geometric function can be analytically continuated to the whole complex plain except $e^{\pm i\pi/3}$

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