Question

Evaluating an integral by substitution and special functions

score 114 · Answer 1 · 2016-03-03 22:32:35

114

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Evaluating an integral by substitution and special functions

Published on 03 Mar 2016 - 22:32

score 1.6k · Answer 2 · 2016-03-04 15:47:48

1.6k

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Proving the multiplication formula of Gamma function

Published on 04 Mar 2016 - 15:47

score 577 · Answer 3 · 2016-03-07 14:40:45

577

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How to prove $\int_{0} ^{1}{\sqrt{1-x^4}dx}=\frac{1}{12}\sqrt {\frac{2}{\pi}}(\Gamma\left(\frac{1}{4}\right))^2$?

Published on 07 Mar 2016 - 14:40

score 434 · Answer 4 · 2016-03-18 11:42:12

434

Views

Limit involving the inverse beta regularized function

Published on 18 Mar 2016 - 11:42

score 238 · Answer 5 · 2016-03-19 16:03:41

238

Views

Evaluating an integral involving Beta function

Published on 19 Mar 2016 - 16:03

score 65 · Answer 6 · 2016-03-21 05:15:06

65

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Check this value of $\int_{0}^{x}\frac{t^m}{(x-t)^\alpha}dt$

Published on 21 Mar 2016 - 5:15

score 398 · Answer 7 · 2016-03-31 18:31:45

398

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Is it possible to integrate $\int_0^1 x^5 (2-x)^4 \text dx$ using Beta functions?

Published on 31 Mar 2016 - 18:31

score 177 · Answer 8 · 2016-04-04 12:30:51

177

Views

Calculating $f(x), f(x\mid y), f(y\mid x)$ from $f(x,y)\propto \left(\begin{array}n n\\ x\end{array}\right)y^{x+\alpha-1}(1-y)^{n-x+\beta-1}$

Published on 04 Apr 2016 - 12:30

score 394 · Answer 9 · 2016-04-05 19:07:57

394

Views

Write area in terms of Gamma function

Published on 05 Apr 2016 - 19:07

score 152 · Answer 10 · 2016-04-13 06:06:16

152

Views

2nd moment of the Beta Function / Beta function simplification

Published on 13 Apr 2016 - 6:06

score 159 · Answer 11 · 2016-04-15 18:54:19

159

Views

Beta function. What is wrong? Misunderstanding.

Published on 15 Apr 2016 - 18:54

score 112 · Answer 12 · 2016-04-20 13:34:27

112

Views

Finite series that gives Beta function at integers

Published on 20 Apr 2016 - 13:34

score 150 · Answer 13 · 2016-04-25 17:01:08

150

Views

When is the inequality $\beta(a_1+b_1, a_2+b_2)\ge \beta(a_1, a_2)\beta(b_1, b_2)$ true?

Published on 25 Apr 2016 - 17:01

score 1.8k · Answer 14 · 2016-04-26 14:57:46

1.8k

Views

Expected value of exponential function

Published on 26 Apr 2016 - 14:57

score 1.2k · Answer 15 · 2016-05-04 21:30:30

1.2k

Views

Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

Published on 04 May 2016 - 21:30

List Question

Evaluating an integral by substitution and special functions

Proving the multiplication formula of Gamma function

How to prove $\int_{0} ^{1}{\sqrt{1-x^4}dx}=\frac{1}{12}\sqrt {\frac{2}{\pi}}(\Gamma\left(\frac{1}{4}\right))^2$?

Limit involving the inverse beta regularized function

Evaluating an integral involving Beta function

Check this value of $\int_{0}^{x}\frac{t^m}{(x-t)^\alpha}dt$

Is it possible to integrate $\int_0^1 x^5 (2-x)^4 \text dx$ using Beta functions?

Calculating $f(x), f(x\mid y), f(y\mid x)$ from $f(x,y)\propto \left(\begin{array}n n\\ x\end{array}\right)y^{x+\alpha-1}(1-y)^{n-x+\beta-1}$

Write area in terms of Gamma function

2nd moment of the Beta Function / Beta function simplification

Beta function. What is wrong? Misunderstanding.

Finite series that gives Beta function at integers

When is the inequality $\beta(a_1+b_1, a_2+b_2)\ge \beta(a_1, a_2)\beta(b_1, b_2)$ true?

Expected value of exponential function

Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

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