User David H

28 votes

4 answers

915 views

Integrals of integer powers of dilogarithm function

asked Aug 29, 2014 at 2:27

28 votes

1 answer

999 views

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

integration definite-integrals closed-form hypergeometric-function elliptic-integrals

asked Oct 25, 2014 at 2:44

24 votes

2 answers

555 views

Definite integral of arcsine over square-root of quadratic

definite-integrals special-functions closed-form hypergeometric-function polylogarithm

asked May 27, 2015 at 2:58

18 votes

3 answers

567 views

Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

integration definite-integrals logarithms improper-integrals closed-form

asked Jun 27, 2014 at 22:49

17 votes

3 answers

2k views

How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

integration definite-integrals improper-integrals closed-form

asked Jun 12, 2014 at 3:42

12 votes

3 answers

1k views

How to demonstrate the equality of these integral representations of $\pi$?

calculus integration definite-integrals improper-integrals pi

asked Dec 18, 2013 at 20:49

11 votes

2 answers

2k views

Closed form for integral of integer powers of Sinc function

integration definite-integrals special-functions improper-integrals closed-form

asked Aug 12, 2014 at 2:51

10 votes

4 answers

576 views

Evaluation of a dilogarithmic integral

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

asked Aug 23, 2014 at 4:10

9 votes

2 answers

245 views

Indefinite integral typo in Gradshteĭn: reciprocal square-root of sixth degree polynomial

integration indefinite-integrals elliptic-integrals

asked Sep 7, 2014 at 21:25

8 votes

2 answers

329 views

Closed form for $\int z^n\ln{(z)}\ln{(1-z)}\,\mathrm{d}z$?

integration logarithms special-functions indefinite-integrals polylogarithm

asked Sep 16, 2014 at 3:15

8 votes

2 answers

451 views

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

integration definite-integrals closed-form hypergeometric-function

asked Dec 31, 2014 at 17:28

8 votes

1 answer

274 views

Another polylog integral

definite-integrals closed-form polylogarithm

asked Nov 30, 2015 at 1:06

7 votes

1 answer

255 views

Challenging definite integral of hypergeometric functions

integration definite-integrals special-functions closed-form hypergeometric-function

asked Aug 12, 2016 at 17:20

7 votes

2 answers

290 views

Prove: $\int_{0}^{1}\frac{\ln{x}\,\mathrm{d}x}{\sqrt[3]{x(1-x^2)^2}}\stackrel{?}{=}-\frac18\left[\Gamma{\left(\frac13\right)}\right]^3$

integration definite-integrals logarithms special-functions hypergeometric-function

asked Aug 24, 2014 at 6:47

7 votes

3 answers

683 views

Proofs without words of some well-known historical values of $\pi$?

geometry circles math-history pi visualization

asked Nov 23, 2013 at 1:22

6 votes

2 answers

370 views

Prove this polylogarithmic integral has the stated closed form value

integration definite-integrals logarithms closed-form polylogarithm

asked Jul 19, 2014 at 23:00

6 votes

3 answers

589 views

Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

integration definite-integrals special-functions closed-form hypergeometric-function

asked Dec 22, 2015 at 5:01

5 votes

0 answers

152 views

Verifying closed form evaluation of an Ising-class multiple integral

integration definite-integrals special-functions closed-form polylogarithm

asked Oct 14, 2016 at 1:34

5 votes

1 answer

260 views

Seeking closed-form solution to $\sum_{n=1}^{\infty}\frac{\log{(1+n)}}{(1+n)^{\alpha}-1}$

sequences-and-series closed-form

asked Jun 16, 2014 at 8:54

5 votes

1 answer

351 views

Simplifying a certain polylogarithmic sum in two variables

calculus definite-integrals special-functions closed-form polylogarithm

asked Sep 17, 2015 at 6:14

5 votes

1 answer

793 views

Simplifying real part of hypergeometric function with complex parameters

definite-integrals special-functions closed-form hypergeometric-function bessel-functions

asked Jun 26, 2015 at 0:04

4 votes

1 answer

439 views

Extending the rationals using exponentiation

exponentiation irrational-numbers rational-numbers

asked Mar 15, 2013 at 5:43

4 votes

1 answer

100 views

Closed form evaluation of a trigonometric integral in terms of polylogarithms

definite-integrals special-functions closed-form trigonometric-integrals polylogarithm

asked Oct 22, 2021 at 16:37

3 votes

1 answer

139 views

Factoring the quartic $\left(x^{2}+x-1\right)\left(x^{2}+2x-1\right)-2sx\left(2x-1\right)^{2}$

calculus polynomials roots factoring

asked Dec 19, 2015 at 21:40

3 votes

1 answer

406 views

Evaluating a double integral of a complicated rational function

calculus integration multivariable-calculus definite-integrals closed-form

asked Dec 28, 2016 at 18:59

3 votes

1 answer

146 views

Closed form of a trigonometric integral sought

integration trigonometry definite-integrals closed-form

asked Jun 11, 2014 at 19:24

3 votes

1 answer

183 views

Evaluating a logarithmic integral in terms of trilogarithms

integration definite-integrals special-functions polylogarithm

asked Sep 10, 2015 at 3:56

2 votes

1 answer

1k views

Need help understanding a certain vector integral identity (Stokes' theorem corollary)

integration multivariable-calculus vector-analysis

asked Jun 13, 2014 at 20:04

2 votes

0 answers

174 views

Reduction of a type of elliptic integral to Legendre normal form

integration definite-integrals improper-integrals elliptic-integrals cauchy-principal-value

asked Jul 3, 2019 at 23:16

2 votes

2 answers

155 views

Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)

integration complex-analysis definite-integrals closed-form polylogarithm

asked Jul 11, 2020 at 10:22

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33 Questions

Integrals of integer powers of dilogarithm function

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

Definite integral of arcsine over square-root of quadratic

Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

How to demonstrate the equality of these integral representations of $\pi$?

Closed form for integral of integer powers of Sinc function

Evaluation of a dilogarithmic integral

Indefinite integral typo in Gradshteĭn: reciprocal square-root of sixth degree polynomial

Closed form for $\int z^n\ln{(z)}\ln{(1-z)}\,\mathrm{d}z$?

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

Another polylog integral

Challenging definite integral of hypergeometric functions

Prove: $\int_{0}^{1}\frac{\ln{x}\,\mathrm{d}x}{\sqrt[3]{x(1-x^2)^2}}\stackrel{?}{=}-\frac18\left[\Gamma{\left(\frac13\right)}\right]^3$

Proofs without words of some well-known historical values of $\pi$?

Prove this polylogarithmic integral has the stated closed form value

Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

Verifying closed form evaluation of an Ising-class multiple integral

Seeking closed-form solution to $\sum_{n=1}^{\infty}\frac{\log{(1+n)}}{(1+n)^{\alpha}-1}$

Simplifying a certain polylogarithmic sum in two variables

Simplifying real part of hypergeometric function with complex parameters

Extending the rationals using exponentiation

Closed form evaluation of a trigonometric integral in terms of polylogarithms

Factoring the quartic $\left(x^{2}+x-1\right)\left(x^{2}+2x-1\right)-2sx\left(2x-1\right)^{2}$

Evaluating a double integral of a complicated rational function

Closed form of a trigonometric integral sought

Evaluating a logarithmic integral in terms of trilogarithms

Need help understanding a certain vector integral identity (Stokes' theorem corollary)

Reduction of a type of elliptic integral to Legendre normal form

Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)