Question

Integration involving product of Bessel K's, polynomial and exponential

score 117 · Answer 1 · 2026-04-14 01:21:15

117

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Integration involving product of Bessel K's, polynomial and exponential

Published on 14 Apr 2026 - 1:21

score 101 · Answer 2 · 2026-04-16 23:50:15

101

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Why $\frac{(-i)^n}{\sqrt{2\pi}} \int_{-\infty}^\infty \sqrt{x^2+p^2} e^{ipx} H_n(p) e^{-p^2/2} dp \approx \sqrt{2n+1} H_n(x) e^{-x^2/2}$?

Published on 16 Apr 2026 - 23:50

score 102 · Answer 3 · 2026-04-12 06:52:29

102

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Analytical solution to the equation $\sin(n \theta) / \sin(m \theta) = a$.

Published on 12 Apr 2026 - 6:52

score 68 · Answer 4 · 2026-04-12 06:44:41

68

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Proof of Duplication formula for General Clausen function

Published on 12 Apr 2026 - 6:44

score 211 · Answer 5 · 2026-04-14 02:41:05

211

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What is the integral of a product of four Bessel functions, a power, and a Gaussian?

Published on 14 Apr 2026 - 2:41

score 42 · Answer 6 · 2026-04-16 11:49:51

42

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$\sum _{k=0}^{\infty } \sum _{v=0}^{\infty } \frac{ (a+b x)^k (a-b x)^v}{(k!)^2 v!}U(v+1,k+v+2,x)$ with $U$ being confluent hypergeometric function

Published on 16 Apr 2026 - 11:49

score 153 · Answer 7 · 2026-04-14 13:36:27

153

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Integral involving product of dilogarithm and an exponential

Published on 14 Apr 2026 - 13:36

score 117 · Answer 8 · 2026-04-14 22:43:03

117

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Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$

Published on 14 Apr 2026 - 22:43

score 145 · Answer 9 · 2026-04-16 11:38:17

145

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Showing that $\int_0^{\infty} J_n(bx) dx = 1/b$

Published on 16 Apr 2026 - 11:38

score 358 · Answer 10 · 2026-04-14 07:34:27

358

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A definite integral in the Bessel function $J_{-1/2}(s)$ from Stein-Shakarchi

Published on 14 Apr 2026 - 7:34

score 135 · Answer 11 · 2026-04-17 11:42:48

135

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Asymptotic approximation of $_{2}F_{1}(\{1/2- n/2, -n/2\},\{3/2 - n\};z\}$ for $-1/z\rightarrow0$

Published on 17 Apr 2026 - 11:42

score 425 · Answer 12 · 2026-04-10 20:15:03

425

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Integral of Bessel function, power, and hyperbolic cosecant

Published on 10 Apr 2026 - 20:15

score 264 · Answer 13 · 2026-04-16 14:04:53

264

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Approximations of $\sum_{n=0}^\infty\frac{x^n}{n!}$ and $\sum_{n=0}^\infty\frac{x^n}{n!^2}$

Published on 16 Apr 2026 - 14:04

score 97 · Answer 14 · 2026-04-13 01:57:39

97

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Absolute value and modified Bessel function

Published on 13 Apr 2026 - 1:57

score 119 · Answer 15 · 2026-04-15 05:57:19

119

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Which equations can be solved by Boost C++ library’s ibeta_inva, ibeta_invb, and gamma_q_inva functions?

Published on 15 Apr 2026 - 5:57

List Question

Integration involving product of Bessel K's, polynomial and exponential

Why $\frac{(-i)^n}{\sqrt{2\pi}} \int_{-\infty}^\infty \sqrt{x^2+p^2} e^{ipx} H_n(p) e^{-p^2/2} dp \approx \sqrt{2n+1} H_n(x) e^{-x^2/2}$?

Analytical solution to the equation $\sin(n \theta) / \sin(m \theta) = a$.

Proof of Duplication formula for General Clausen function

What is the integral of a product of four Bessel functions, a power, and a Gaussian?

$\sum _{k=0}^{\infty } \sum _{v=0}^{\infty } \frac{ (a+b x)^k (a-b x)^v}{(k!)^2 v!}U(v+1,k+v+2,x)$ with $U$ being confluent hypergeometric function

Integral involving product of dilogarithm and an exponential

Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$

Showing that $\int_0^{\infty} J_n(bx) dx = 1/b$

A definite integral in the Bessel function $J_{-1/2}(s)$ from Stein-Shakarchi

Asymptotic approximation of $_{2}F_{1}(\{1/2- n/2, -n/2\},\{3/2 - n\};z\}$ for $-1/z\rightarrow0$

Integral of Bessel function, power, and hyperbolic cosecant

Approximations of $\sum_{n=0}^\infty\frac{x^n}{n!}$ and $\sum_{n=0}^\infty\frac{x^n}{n!^2}$

Absolute value and modified Bessel function

Which equations can be solved by Boost C++ library’s ibeta_inva, ibeta_invb, and gamma_q_inva functions?

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