List questions from special-functions

Published on 26 Mar 2026 - 11:18

156

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Domain of $\arccos(x)$

Published on 17 Jun 2020 - 6:58

145

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A lower bound for the cosine integral

Published on 25 Mar 2026 - 22:23

446

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History of Gamma and Beta functions

Published on 26 Mar 2026 - 11:17

103

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bound for the ratio of Gamma functions

Published on 01 Apr 2026 - 12:07

87

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Integral $\int_{0}^{1} \frac{x e^{-cx}}{\sqrt{1-x^2}}\,dx$ (possibly using modified Bessel function)?

Published on 29 Mar 2026 - 7:30

539

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Derive the recurrence relations

Published on 24 Jun 2020 - 20:17

399

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Asymptotic expansion of integral involving Bessel Function and Logarithm

Published on 29 Mar 2026 - 7:36

63

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Equations via Lambert's W function

Published on 26 Mar 2026 - 6:18

69

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$\int_0^{\infty} a \sqrt{a^2-b^2} \exp \left[ -\frac{a}{c} \right] da= cb^2K_2 \left[ \frac{b}{c} \right]$

Published on 29 Mar 2026 - 7:37

69

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Why is the Airy function defined with the pre-factor $(2\pi i)^{-1}$? For normalisation?

Published on 30 Jun 2020 - 8:23

104

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Convolution using Integral Transforms

Published on 25 Mar 2026 - 14:18

407

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Solving a sum using the hypergeometric function

Published on 28 Mar 2026 - 14:37

378

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Prove $\, _6F_5\left(\{\frac12\}_5,\frac{5}{4};\frac{1}{4},\{1\}_4;-1\right)=\frac{2}{\Gamma \left(\frac{3}{4}\right)^4}$ and another

Published on 28 Mar 2026 - 14:44

176

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Proving a formula for $\int_{x=0}^\infty \frac{\sin(ax)x}{(x^2+1)^c} dx$ involving Gamma and Bessel K functions

Published on 06 Jul 2020 - 8:18

List Question

Is there a way of solving $I_x^{-1}(a_1,b_1)w_1+I_x^{-1}(a_2,b_2)w_2=k$?

Domain of $\arccos(x)$

A lower bound for the cosine integral

History of Gamma and Beta functions

bound for the ratio of Gamma functions

Integral $\int_{0}^{1} \frac{x e^{-cx}}{\sqrt{1-x^2}}\,dx$ (possibly using modified Bessel function)?

Derive the recurrence relations

Asymptotic expansion of integral involving Bessel Function and Logarithm

Equations via Lambert's W function

$\int_0^{\infty} a \sqrt{a^2-b^2} \exp \left[ -\frac{a}{c} \right] da= cb^2K_2 \left[ \frac{b}{c} \right]$

Why is the Airy function defined with the pre-factor $(2\pi i)^{-1}$? For normalisation?

Convolution using Integral Transforms

Solving a sum using the hypergeometric function

Prove $\, _6F_5\left(\{\frac12\}_5,\frac{5}{4};\frac{1}{4},\{1\}_4;-1\right)=\frac{2}{\Gamma \left(\frac{3}{4}\right)^4}$ and another

Proving a formula for $\int_{x=0}^\infty \frac{\sin(ax)x}{(x^2+1)^c} dx$ involving Gamma and Bessel K functions

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