List questions from special-functions

Published on 26 May 2016 - 11:40

41

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Show that $\int_{1}^{\infty}\frac{x-\left \lfloor x \right \rfloor -\frac{1}{2}}{x^{s+1}}(1-s\log x)\,\mathrm{d}x$ is convergent for $\Re s > -1$

Published on 28 May 2016 - 17:29

222

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Question on the definition of dirac delta function

Published on 08 Apr 2026 - 17:33

61

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Are these Infinite Series Representations of Special Functions?

Published on 29 May 2016 - 0:52

459

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Upper bound for ratio of modified Bessel functions of second kind

Published on 08 Apr 2026 - 6:34

3.1k

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Verify $y=x^aZ_p\left(bx^c\right)$ is a solution to $y''+\left(\frac{1-2a}{x}\right)y'+\left[(bcx^{c-1})^2+\frac{a^2-p^2c^2}{x^2}\right]y=0$

Published on 01 Apr 2026 - 18:50

220

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Equivalent of Jacobi elliptic functions

Published on 27 Mar 2026 - 0:03

177

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Solving $y^y = x$ for large $x$

Published on 29 May 2016 - 19:16

489

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Integral ${\large\int}_0^\infty\big(2J_0(2x)^2+2Y_0(2x)^2-J_0(x)^2-Y_0(x)^2\big)\,dx$

Published on 01 Apr 2026 - 18:50

127

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Approximation of $\ln(x+1)$ with $\Psi$ function

Published on 08 Apr 2026 - 6:26

257

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How to prove that $e^{-\gamma}=\prod_{n=1}^\infty\left(1+\frac1n\right)e^{-1/n}$

Published on 02 Apr 2026 - 9:15

52

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Incomplete Gamma Asymptotics

Published on 07 Apr 2026 - 16:56

147

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Solving a functional equation $2 f(2x)=f(x)(1+\cos(x))+f(x+\pi)(1-\cos(x))$

Published on 06 Apr 2026 - 6:32

724

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What is the motivation behind the Bessel function of second kind

Published on 01 Apr 2026 - 20:25

302

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The Bessel function and finding expression

Published on 08 Apr 2026 - 16:37

List Question

Limit of trig functions

Show that $\int_{1}^{\infty}\frac{x-\left \lfloor x \right \rfloor -\frac{1}{2}}{x^{s+1}}(1-s\log x)\,\mathrm{d}x$ is convergent for $\Re s > -1$

Question on the definition of dirac delta function

Are these Infinite Series Representations of Special Functions?

Upper bound for ratio of modified Bessel functions of second kind

Verify $y=x^aZ_p\left(bx^c\right)$ is a solution to $y''+\left(\frac{1-2a}{x}\right)y'+\left[(bcx^{c-1})^2+\frac{a^2-p^2c^2}{x^2}\right]y=0$

Equivalent of Jacobi elliptic functions

Solving $y^y = x$ for large $x$

Integral ${\large\int}_0^\infty\big(2J_0(2x)^2+2Y_0(2x)^2-J_0(x)^2-Y_0(x)^2\big)\,dx$

Approximation of $\ln(x+1)$ with $\Psi$ function

How to prove that $e^{-\gamma}=\prod_{n=1}^\infty\left(1+\frac1n\right)e^{-1/n}$

Incomplete Gamma Asymptotics

Solving a functional equation $2 f(2x)=f(x)(1+\cos(x))+f(x+\pi)(1-\cos(x))$

What is the motivation behind the Bessel function of second kind

The Bessel function and finding expression

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