Question

Integral of powers of Bessel function from 0 to infinity

score 234 · Answer 1 · 2026-04-14 13:36:44

234

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Integral of powers of Bessel function from 0 to infinity

Published on 14 Apr 2026 - 13:36

score 104 · Answer 2 · 2026-03-25 15:58:55

104

Views

What functions do we need to solve linear second order differential equations with polynomial coeficients?

Published on 25 Mar 2026 - 15:58

score 64 · Answer 3 · 2026-04-11 19:39:46

64

Views

Solutions to Bessel Differential Equations

Published on 11 Apr 2026 - 19:39

score 47 · Answer 4 · 2026-04-12 22:06:01

47

Views

Obtaining the most important terms in a certain spherical integral involving Hermite polynomials

Published on 12 Apr 2026 - 22:06

score 122 · Answer 5 · 2026-04-12 23:37:03

122

Views

Compute the sum of series with coefficients in terms of $\Gamma$

Published on 12 Apr 2026 - 23:37

score 189 · Answer 6 · 2026-04-17 02:45:13

189

Views

Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

Published on 17 Apr 2026 - 2:45

score 63 · Answer 7 · 2026-04-16 17:23:56

63

Views

Find coefficient of $t^k$ in $\int_0^{2\pi}H_n(t\cos\phi+(1-t^2)^{1/2}\sin\phi)H_m(r\cos\phi)d\phi$, where $H_n$ is $n$th Hermite polynomial

Published on 16 Apr 2026 - 17:23

score 50 · Answer 8 · 2026-04-15 22:01:13

50

Views

Analytic formula for $\int_0^{2\pi} \cos^N\phi H_n(r\cos\phi)\sin^M\phi H_m(r\sin\phi)d\phi$, where $H_n$ is $n$th Hermite polynomial

Published on 15 Apr 2026 - 22:01

score 66 · Answer 9 · 2026-04-20 03:17:31

66

Views

Show that $J_0(x) + 2\sum_{n = 1}^\infty J_{2n}(x) = 1$

Published on 20 Apr 2026 - 3:17

score 86 · Answer 10 · 2026-04-16 12:10:28

86

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Find the arc length $\int_ 0 ^{4\pi} r(t)=3\cos ti+4\sin tkj+tk$

Published on 16 Apr 2026 - 12:10

score 241 · Answer 11 · 2026-04-16 17:01:07

241

Views

Asymptotic integration of $\int_0^\infty\frac{x^{-\frac{1}{2}+a}J_{-\frac{1}{2}+a}(x\alpha)}{e^x-1}{\rm d}x$ when $\alpha \gg 1$

Published on 16 Apr 2026 - 17:01

score 37 · Answer 12 · 2026-04-14 20:58:46

37

Views

Show that the Sequence of $\mathrm{Si}((2m+1)\pi)_{m\in\mathbb{N}_0 }$ is monotonically decreasing

Published on 14 Apr 2026 - 20:58

score 196 · Answer 13 · 2026-04-12 10:28:53

196

Views

Double integral over modified Bessel function of the second kind of zeroth order

Published on 12 Apr 2026 - 10:28

score 276 · Answer 14 · 2026-04-14 00:25:15

276

Views

asymptotic for the complex exponential integral Ei(s)

Published on 14 Apr 2026 - 0:25

score 219 · Answer 15 · 2026-04-16 03:34:18

219

Views

Asymptotic power series expansion of $\int_0^\infty\frac{x^\nu J_\nu(x\alpha)}{e^x-1}{\rm d}x$ around $\alpha=1$ and $\alpha<1$

Published on 16 Apr 2026 - 3:34

List Question

Integral of powers of Bessel function from 0 to infinity

What functions do we need to solve linear second order differential equations with polynomial coeficients?

Solutions to Bessel Differential Equations

Obtaining the most important terms in a certain spherical integral involving Hermite polynomials

Compute the sum of series with coefficients in terms of $\Gamma$

Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

Find coefficient of $t^k$ in $\int_0^{2\pi}H_n(t\cos\phi+(1-t^2)^{1/2}\sin\phi)H_m(r\cos\phi)d\phi$, where $H_n$ is $n$th Hermite polynomial

Analytic formula for $\int_0^{2\pi} \cos^N\phi H_n(r\cos\phi)\sin^M\phi H_m(r\sin\phi)d\phi$, where $H_n$ is $n$th Hermite polynomial

Show that $J_0(x) + 2\sum_{n = 1}^\infty J_{2n}(x) = 1$

Find the arc length $\int_ 0 ^{4\pi} r(t)=3\cos ti+4\sin tkj+tk$

Asymptotic integration of $\int_0^\infty\frac{x^{-\frac{1}{2}+a}J_{-\frac{1}{2}+a}(x\alpha)}{e^x-1}{\rm d}x$ when $\alpha \gg 1$

Show that the Sequence of $\mathrm{Si}((2m+1)\pi)_{m\in\mathbb{N}_0 }$ is monotonically decreasing

Double integral over modified Bessel function of the second kind of zeroth order

asymptotic for the complex exponential integral Ei(s)

Asymptotic power series expansion of $\int_0^\infty\frac{x^\nu J_\nu(x\alpha)}{e^x-1}{\rm d}x$ around $\alpha=1$ and $\alpha<1$

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