List questions from special-functions

Published on 25 Mar 2026 - 15:56

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Prove: $\sin (3\pi/2 - x) = -\cos(x)$

Published on 19 May 2014 - 16:55

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Reduction of DEs to Bessel equation

Published on 20 May 2014 - 8:35

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How prove this $p(x)>0$ if $p(x)=\sum_{i=0}^{n}\binom{n}{i}a_{i}x^i(1-x)^{n-i}$

Published on 20 May 2014 - 15:03

142

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integral involving hypergeometric function $\int^1_0\frac{_2F_1(p,p;p+1;-\frac{1}{y})}{y}\,dy$

Published on 20 May 2014 - 16:13

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Inverse logarithmic integral

Published on 21 May 2014 - 14:02

2.7k

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Integral involving the spherical Bessel function of the first kind: $\int_{0}^{\infty} x^{-n}j_{n+1}(x) \, dx$

Published on 28 Mar 2026 - 4:53

191

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Log Log Integrals II

Published on 25 Mar 2026 - 22:01

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Infinite sum of Bessel Functions

Published on 23 May 2014 - 0:01

253

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Equailty involving Elliptic integrals and hypergeometric function

Published on 23 May 2014 - 15:27

362

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Proof that $J_{\nu}(x) \sim (x/2)^\nu / \Gamma(\nu+1) \; \text{as} \; \nu \rightarrow \infty$

Published on 24 May 2014 - 3:16

659

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Integral $\int_0^\infty \frac{\cos x}{x}\left(\int_0^x \frac{\sin t}{t}dt\right)^2dx=-\frac{7}{6}\zeta(3)$

Published on 24 May 2014 - 23:12

343

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Continuous non differentiable functions :)

Published on 25 May 2014 - 0:34

1k

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Elliptic integral $\int^1_0 \frac{K(k)}{\sqrt{1-k^2}}\,dk$

Published on 25 Mar 2026 - 16:02

166

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How to reproduce the Mathematica solution for $\int(\cos x)^{\frac23}dx$?

Published on 29 Mar 2026 - 23:59

List Question

Log Log Integrals III

Prove: $\sin (3\pi/2 - x) = -\cos(x)$

Reduction of DEs to Bessel equation

How prove this $p(x)>0$ if $p(x)=\sum_{i=0}^{n}\binom{n}{i}a_{i}x^i(1-x)^{n-i}$

integral involving hypergeometric function $\int^1_0\frac{_2F_1(p,p;p+1;-\frac{1}{y})}{y}\,dy$

Inverse logarithmic integral

Integral involving the spherical Bessel function of the first kind: $\int_{0}^{\infty} x^{-n}j_{n+1}(x) \, dx$

Log Log Integrals II

Infinite sum of Bessel Functions

Equailty involving Elliptic integrals and hypergeometric function

Proof that $J_{\nu}(x) \sim (x/2)^\nu / \Gamma(\nu+1) \; \text{as} \; \nu \rightarrow \infty$

Integral $\int_0^\infty \frac{\cos x}{x}\left(\int_0^x \frac{\sin t}{t}dt\right)^2dx=-\frac{7}{6}\zeta(3)$

Continuous non differentiable functions :)

Elliptic integral $\int^1_0 \frac{K(k)}{\sqrt{1-k^2}}\,dk$

How to reproduce the Mathematica solution for $\int(\cos x)^{\frac23}dx$?

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