Question

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

score 176 · Answer 1 · 2026-04-11 18:11:15

176

Views

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Published on 11 Apr 2026 - 18:11

score 96 · Answer 2 · 2026-04-09 13:22:47

96

Views

Interchanging summations over sets

Published on 09 Apr 2026 - 13:22

score 113 · Answer 3 · 2023-05-08 04:38:29

113

Views

Why does Fubini's theorem not work in $\int_2^4\int_{x/2}^\sqrt{x}xy\ dy\ dx$?

Published on 08 May 2023 - 4:38

score 66 · Answer 4 · 2023-05-09 14:50:07

66

Views

Use of Fubini's theorem to check if equalities holds

Published on 09 May 2023 - 14:50

score 17 · Answer 5 · 2026-04-12 07:33:41

17

Views

Show that $E(Y)-E(X)=\int_{-\infty}^\infty[P(X<t\le Y)-P(Y<t\le X)]\lambda(dt)$

Published on 12 Apr 2026 - 7:33

score 50 · Answer 6 · 2026-04-12 13:31:26

50

Views

Double integral of $f(x,y)=\frac{xy}{(1-|x|)^2+(1-|y|)^2)}$ on $[-1,1] \times [-1,1]$

Published on 12 Apr 2026 - 13:31

score 39 · Answer 7 · 2026-04-14 02:59:33

39

Views

multivariate integral of a function defined by an inner product

Published on 14 Apr 2026 - 2:59

score 24 · Answer 8 · 2023-05-24 16:04:05

24

Views

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score 81 · Answer 9 · 2026-04-12 11:34:27

81

Views

Equality of expected value using Fubini's theorem

Published on 12 Apr 2026 - 11:34

score 459 · Answer 10 · 2023-06-03 23:48:51

459

Views

Show $\int_0^{\pi/2}\int_0^1 e^{t+t^{\tan\theta}}dtd\theta=\frac{\pi}{4}(e^2-1)$

Published on 03 Jun 2023 - 23:48

score 53 · Answer 11 · 2023-06-06 21:13:36

53

Views

Iterated integral where the density is not continous at the limit of integration

Published on 06 Jun 2023 - 21:13

score 103 · Answer 12 · 2023-06-07 07:27:06

103

Views

Show that $\sum_{(n,m)\in A\times B}x_{n,m}=\sum_{n\in A}\sum_{m\in B}x_{n,m}=\sum_{m\in B}\sum_{n\in A}x_{n,m}.$ Tao's Introduction to Measure Theory

Published on 07 Jun 2023 - 7:27

score 79 · Answer 13 · 2026-04-11 20:49:11

79

Views

Can I change the order of integration when the upper limits are infinite?

Published on 11 Apr 2026 - 20:49

score 53 · Answer 14 · 2023-07-10 07:34:23

53

Views

Fubini theorem on non-$\Sigma$-finite measures

Published on 10 Jul 2023 - 7:34

score 190 · Answer 15 · 2026-04-11 12:56:33

190

Views

Application of Fubini's Theorem - showing an integral-defined operator on $L^p$ outputs measurable functions

Published on 11 Apr 2026 - 12:56

List Question

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Interchanging summations over sets

Why does Fubini's theorem not work in $\int_2^4\int_{x/2}^\sqrt{x}xy\ dy\ dx$?

Use of Fubini's theorem to check if equalities holds

Show that $E(Y)-E(X)=\int_{-\infty}^\infty[P(X<t\le Y)-P(Y<t\le X)]\lambda(dt)$

Double integral of $f(x,y)=\frac{xy}{(1-|x|)^2+(1-|y|)^2)}$ on $[-1,1] \times [-1,1]$

multivariate integral of a function defined by an inner product

Clarification with regards to Fubini

Equality of expected value using Fubini's theorem

Show $\int_0^{\pi/2}\int_0^1 e^{t+t^{\tan\theta}}dtd\theta=\frac{\pi}{4}(e^2-1)$

Iterated integral where the density is not continous at the limit of integration

Show that $\sum_{(n,m)\in A\times B}x_{n,m}=\sum_{n\in A}\sum_{m\in B}x_{n,m}=\sum_{m\in B}\sum_{n\in A}x_{n,m}.$ Tao's Introduction to Measure Theory

Can I change the order of integration when the upper limits are infinite?

Fubini theorem on non-$\Sigma$-finite measures

Application of Fubini's Theorem - showing an integral-defined operator on $L^p$ outputs measurable functions

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