User David H

12

27

votes

4

answers

588

views

Integrals of integer powers of dilogarithm function

May 5 '17 at 12:51 Przemo 5,144

8

26

votes

1

answer

696

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 improper-integrals hypergeometric-function elliptic-integrals

Jan 29 '15 at 2:40 David H 22.4k

4

25

votes

2

answers

444

views

Definite integral of arcsine over square-root of quadratic

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

Oct 4 '17 at 12:34 Przemo 5,144

12

17

votes

3

answers

501

views

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

integration definite-integrals logarithms improper-integrals closed-form

Jun 28 '14 at 18:08 Cody 8,246

7

17

votes

3

answers

818

views

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

integration definite-integrals improper-integrals closed-form

Jun 13 '14 at 21:39 Cody 8,246

10

12

votes

2

answers

1k

views

Closed form for integral of integer powers of Sinc function

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

Dec 20 '14 at 7:12 zs_int 116

11

10

votes

3

answers

426

views

Evaluation of a dilogarithmic integral

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

Jun 20 '17 at 11:31 Przemo 5,144

3

10

votes

3

answers

942

views

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

calculus integration definite-integrals improper-integrals pi

Aug 7 '14 at 9:04 David H 22.4k

2

9

votes

2

answers

184

views

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

integration indefinite-integrals elliptic-integrals

Jan 29 '15 at 0:18 David H 22.4k

2

8

votes

1

answer

153

views

Another polylog integral

definite-integrals closed-form polylogarithm

Apr 26 '17 at 23:21 Felix Marin 71.3k

7

8

votes

2

answers

241

views

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

integration definite-integrals closed-form hypergeometric-function

Jan 2 '15 at 16:49 user111187 4,073

1

8

votes

2

answers

174

views

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

integration logarithms special-functions indefinite-integrals polylogarithm

Sep 16 '14 at 5:50 karvens 3,517

4

7

votes

1

answer

199

views

Challenging definite integral of hypergeometric functions

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

Mar 28 at 3:40 clathratus 6,625

1

7

votes

3

answers

548

views

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

geometry circles math-history pi visualization

Sep 16 '14 at 3:05 Rohan 1

4

7

votes

2

answers

267

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

Aug 24 '14 at 7:31 Jack D'Aurizio 296k

1

6

votes

1

answer

189

views

Simplifying a certain polylogarithmic sum in two variables

calculus definite-integrals special-functions closed-form polylogarithm

May 1 '16 at 11:05 Community♦ 1

6

votes

1

answer

290

views

Prove this polylogarithmic integral has the stated closed form value

integration definite-integrals logarithms closed-form polylogarithm

Jul 25 '14 at 22:02 Random Variable 25.8k

2

5

votes

2

answers

362

views

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

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

Feb 7 '17 at 20:41 Ondrej Hutnik 1

3

5

votes

0

answers

125

views

Verifying closed form evaluation of an Ising-class multiple integral

integration definite-integrals special-functions closed-form polylogarithm

Dec 6 '16 at 22:30 David H 22.4k

2

5

votes

1

answer

235

views

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

sequences-and-series closed-form

May 15 '16 at 20:34 Community♦ 1

5

votes

1

answer

353

views

Simplifying real part of hypergeometric function with complex parameters

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

Jun 26 '15 at 0:40 Leucippus 19.9k

2

4

votes

0

answers

148

views

Double integral of symmetric polylogarithmic function over rectangular region

integration definite-integrals improper-integrals special-functions polylogarithm

Apr 21 '16 at 9:20 David H 22.4k

2

3

votes

1

answer

263

views

Evaluating a double integral of a complicated rational function

calculus integration multivariable-calculus definite-integrals closed-form

May 1 '18 at 16:42 Przemo 5,144

3

votes

1

answer

114

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

Dec 19 '15 at 23:31 tomi 6,592

1

3

votes

1

answer

149

views

Evaluating a logarithmic integral in terms of trilogarithms

integration definite-integrals special-functions polylogarithm

Sep 10 '15 at 18:16 David H 22.4k

1

3

votes

1

answer

134

views

Closed form of a trigonometric integral sought

integration trigonometry definite-integrals closed-form

Jun 11 '14 at 19:41 Community♦ 1

1

3

votes

1

answer

364

views

Extending the rationals using exponentiation

exponentiation irrational-numbers rational-numbers

Apr 9 '13 at 1:57 Alex Kruckman 31.4k

2

votes

1

answer

665

views

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

integration multivariable-calculus vector-analysis

Jun 13 '14 at 23:39 Community♦ 1

1

vote

0

answers

32

views

Reduction of a type of elliptic integral to Legendre normal form

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

Jul 3 at 23:16 David H 22.4k

1

vote

3

answers

231

views

Solving a 2nd-order linear recurrence with variable coefficients

integration definite-integrals recurrence-relations closed-form

Mar 6 '16 at 2:27 David H 22.4k

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30 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: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}$

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

Closed form for integral of integer powers of Sinc function

Evaluation of a dilogarithmic integral

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

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

Another polylog integral

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

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

Challenging definite integral of hypergeometric functions

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

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

Simplifying a certain polylogarithmic sum in two variables

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 real part of hypergeometric function with complex parameters

Double integral of symmetric polylogarithmic function over rectangular region

Evaluating a double integral of a complicated rational function

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

Evaluating a logarithmic integral in terms of trilogarithms

Closed form of a trigonometric integral sought

Extending the rationals using exponentiation

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

Reduction of a type of elliptic integral to Legendre normal form

Solving a 2nd-order linear recurrence with variable coefficients