Question

Bounds on integral $x^{-a} \int_{1}^x y^{a-1} \exp(-y a) dy$

score 288 · Answer 1 · 2026-04-16 23:09:08

288

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Bounds on integral $x^{-a} \int_{1}^x y^{a-1} \exp(-y a) dy$

Published on 16 Apr 2026 - 23:09

score 892 · Answer 2 · 2026-04-12 07:14:32

892

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Fourier Transform of Bessel function with square root argument

Published on 12 Apr 2026 - 7:14

score 4.1k · Answer 3 · 2026-04-12 08:47:36

4.1k

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Bessel function integral and Mellin transform

Published on 12 Apr 2026 - 8:47

score 126 · Answer 4 · 2026-04-12 01:59:09

126

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Why exponentiation is considered elementary funtion?

Published on 12 Apr 2026 - 1:59

score 460 · Answer 5 · 2026-04-10 11:18:30

460

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How to show integral of different order Hankel transformed functions are equal?

Published on 10 Apr 2026 - 11:18

score 8.7k · Answer 6 · 2026-04-12 02:19:24

8.7k

Views

Connection between Legendre polynomial and Bessel function

Published on 12 Apr 2026 - 2:19

score 4.3k · Answer 7 · 2026-04-13 08:03:18

4.3k

Views

Are there well known lower bounds for the upper incomplete gamma function?

Published on 13 Apr 2026 - 8:03

score 255 · Answer 8 · 2026-04-14 09:41:30

255

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Closed form of integral of $\operatorname{erfc} \log t$

Published on 14 Apr 2026 - 9:41

score 598 · Answer 9 · 2026-04-12 23:47:41

598

Views

Was the definition of $\mathrm{erf}$ changed at some point?

Published on 12 Apr 2026 - 23:47

score 2.2k · Answer 10 · 2026-04-16 00:27:05

2.2k

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Proof that $\sum\limits_{k=1}^\infty\frac{a_1a_2\cdots a_{k-1}}{(x+a_1)\cdots(x+a_k)}=\frac{1}{x}$ regarding $\zeta(3)$ and Apéry's proof

Published on 16 Apr 2026 - 0:27

score 415 · Answer 11 · 2026-04-11 13:55:49

415

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Could you give a application of a special function on number theory or analysis?

Published on 11 Apr 2026 - 13:55

score 439 · Answer 12 · 2026-04-13 22:04:40

439

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how to evaluate $\int_0^1\sin(\frac{1}{x})dx$?

Published on 13 Apr 2026 - 22:04

score 672 · Answer 13 · 2026-04-17 22:35:29

672

Views

What is the fractional derivative of the function $\pi \cot (\pi x)$?

Published on 17 Apr 2026 - 22:35

score 496 · Answer 14 · 2026-04-15 09:52:02

496

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A Curious Binomial Coefficient Sum: $\sum_{j = 0}^{k} \binom{k}{j} \binom{j + n -\ell + 1}{n}$

Published on 15 Apr 2026 - 9:52

score 289 · Answer 15 · 2026-04-17 07:34:15

289

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Can it be shown that $Y_0(\lambda_n a)J_0(\lambda_n a) - J_0(\lambda_n a)Y_0(\lambda_n a) \ne 0$?

Published on 17 Apr 2026 - 7:34

List Question

Bounds on integral $x^{-a} \int_{1}^x y^{a-1} \exp(-y a) dy$

Fourier Transform of Bessel function with square root argument

Bessel function integral and Mellin transform

Why exponentiation is considered elementary funtion?

How to show integral of different order Hankel transformed functions are equal?

Connection between Legendre polynomial and Bessel function

Are there well known lower bounds for the upper incomplete gamma function?

Closed form of integral of $\operatorname{erfc} \log t$

Was the definition of $\mathrm{erf}$ changed at some point?

Proof that $\sum\limits_{k=1}^\infty\frac{a_1a_2\cdots a_{k-1}}{(x+a_1)\cdots(x+a_k)}=\frac{1}{x}$ regarding $\zeta(3)$ and Apéry's proof

Could you give a application of a special function on number theory or analysis?

how to evaluate $\int_0^1\sin(\frac{1}{x})dx$?

What is the fractional derivative of the function $\pi \cot (\pi x)$?

A Curious Binomial Coefficient Sum: $\sum_{j = 0}^{k} \binom{k}{j} \binom{j + n -\ell + 1}{n}$

Can it be shown that $Y_0(\lambda_n a)J_0(\lambda_n a) - J_0(\lambda_n a)Y_0(\lambda_n a) \ne 0$?

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