Question

Are special functions an active field? A mathematician's dilemma.

score 125 · Answer 1 · 2026-04-12 03:17:48

125

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Are special functions an active field? A mathematician's dilemma.

Published on 12 Apr 2026 - 3:17

score 159 · Answer 2 · 2026-04-12 05:45:36

159

Views

Closed form expression for summation and integration

Published on 12 Apr 2026 - 5:45

score 54 · Answer 3 · 2026-04-16 09:19:21

54

Views

Corollary 1.4.4 Roy's "Special Functions" book

Published on 16 Apr 2026 - 9:19

score 131 · Answer 4 · 2026-04-12 00:01:45

131

Views

Fourth order non-constant-coefficients ODE

Published on 12 Apr 2026 - 0:01

score 348 · Answer 5 · 2026-04-14 14:33:12

348

Views

Prove $\displaystyle\sum_{-\infty}^0\text H(x)=\frac12\sum_0^\infty\frac{\text H_\frac x2-\text H_\frac{x-1}2}{x!}=\frac{\text{Ei}(2)-\text{Ei}(1)}e$

Published on 14 Apr 2026 - 14:33

score 81 · Answer 6 · 2026-04-10 20:33:31

81

Views

Some properties of Bessel function of first kind with integer order

Published on 10 Apr 2026 - 20:33

score 89 · Answer 7 · 2026-04-09 15:59:58

89

Views

Asymptotic expansion of integral with Hankel function

Published on 09 Apr 2026 - 15:59

score 133 · Answer 8 · 2026-04-17 22:53:53

133

Views

Evaluate $\int_{\mathbb{R}^n} \left(\frac{\lambda}{\lambda^2+|x|^2}\right)^N dx$

Published on 17 Apr 2026 - 22:53

score 192 · Answer 9 · 2026-04-15 07:25:19

192

Views

On a series representation for a continuous 6j symbol integral: $\large{\int} \small\left\{ \begin{matrix} x&x&x \\ x&x&x \\ \end{matrix}\right \}dx$

Published on 15 Apr 2026 - 7:25

score 289 · Answer 10 · 2026-04-16 14:47:17

289

Views

Conjectured identity involving an elliptic integral and a Bessel function

Published on 16 Apr 2026 - 14:47

score 185 · Answer 11 · 2026-04-14 16:25:08

185

Views

General case for sine integral: $ I = \displaystyle\int_{0}^{\infty}\frac{\sin^{2n+1}{x}}{x}dx $ where $n \in \Bbb N $

Published on 14 Apr 2026 - 16:25

score 73 · Answer 12 · 2026-04-13 22:18:27

73

Views

There exist a functions' space for compact-supported real-valued continuous functions that are smooth except at the boundaries???

Published on 13 Apr 2026 - 22:18

score 125 · Answer 13 · 2026-04-14 10:54:29

125

Views

Is $e^{1-1/(1-(2x)^{2n})},\,|x|\leq 1/2,\,n>1\,integer$ a "Bump Function"?, also, Could be used to define the rectangular function?

Published on 14 Apr 2026 - 10:54

score 81 · Answer 14 · 2026-04-17 09:27:11

81

Views

Integrating $\int_0^{\infty}\log_2(1+q)\exp(-\beta q) \,\mathrm{d}q$

Published on 17 Apr 2026 - 9:27

score 100 · Answer 15 · 2026-04-17 10:51:03

100

Views

How to solve $x=\lim\limits_{t\to0} Q^{-1}(t,t)\implies \text{Ei}(-x)=-1\implies Γ(0,x)=1$?

Published on 17 Apr 2026 - 10:51

List Question

Are special functions an active field? A mathematician's dilemma.

Closed form expression for summation and integration

Corollary 1.4.4 Roy's "Special Functions" book

Fourth order non-constant-coefficients ODE

Prove $\displaystyle\sum_{-\infty}^0\text H(x)=\frac12\sum_0^\infty\frac{\text H_\frac x2-\text H_\frac{x-1}2}{x!}=\frac{\text{Ei}(2)-\text{Ei}(1)}e$

Some properties of Bessel function of first kind with integer order

Asymptotic expansion of integral with Hankel function

Evaluate $\int_{\mathbb{R}^n} \left(\frac{\lambda}{\lambda^2+|x|^2}\right)^N dx$

On a series representation for a continuous 6j symbol integral: $\large{\int} \small\left\{ \begin{matrix} x&x&x \\ x&x&x \\ \end{matrix}\right \}dx$

Conjectured identity involving an elliptic integral and a Bessel function

General case for sine integral: $ I = \displaystyle\int_{0}^{\infty}\frac{\sin^{2n+1}{x}}{x}dx $ where $n \in \Bbb N $

There exist a functions' space for compact-supported real-valued continuous functions that are smooth except at the boundaries???

Is $e^{1-1/(1-(2x)^{2n})},\,|x|\leq 1/2,\,n>1\,integer$ a "Bump Function"?, also, Could be used to define the rectangular function?

Integrating $\int_0^{\infty}\log_2(1+q)\exp(-\beta q) \,\mathrm{d}q$

How to solve $x=\lim\limits_{t\to0} Q^{-1}(t,t)\implies \text{Ei}(-x)=-1\implies Γ(0,x)=1$?

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