equation 7.4.10 from handbook of mathematical functions

Question

Tammun filistin 2018-2-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/381610-equation-7-4-10-from-handbook-of-mathematical-functions

评论： Walter Roberson 2019-5-1

采纳的回答： Birdman

在 MATLAB Online 中打开

dear friends

how i can find the integral in the attached photo by MATLAB

fun = @(t) exp(-t.^2)/(t+1);
q = integral(fun,0,inf)
%%ı tried to write it in this way also but i couldnt have asolution
syms a t x
fun2=exp(-2*t.^2)/(t+1);
sol1 = int(fun2,t,0,inf);

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Walter Roberson 2018-2-8

For x = 1, MATLAB and Maple both give a MeijerG based result; Wolfram Alpha (Mathematica) times out trying to compute it in the free version.

For x not 1, none of the three will find the solution shown -- which, after all, just substitutes one indefinite integral for another.

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Answer 1

Birdman 2018-2-8

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https://ww2.mathworks.cn/matlabcentral/answers/381610-equation-7-4-10-from-handbook-of-mathematical-functions#answer_304186

在 MATLAB Online 中打开

fun = @(t) exp(-t.^2)/(t+1);
q = integral(fun,0,inf,'ArrayValued',true)

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Tammun filistin 2018-2-9

Thank you :)

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Answer 2

Star Strider 2018-2-8

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https://ww2.mathworks.cn/matlabcentral/answers/381610-equation-7-4-10-from-handbook-of-mathematical-functions#answer_304190

在 MATLAB Online 中打开

you need to vectorise the division as well as the exponentiation:

fun = @(t) exp(-t.^2)./(t+1);
                     ↑ ← VECTORIZE HERE AS WELL
q = integral(fun,0,inf)
q =
   0.605133652503344

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Tammun filistin 2018-2-9

Many thanks

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Answer 3

samriti bali 2019-4-29

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https://ww2.mathworks.cn/matlabcentral/answers/381610-equation-7-4-10-from-handbook-of-mathematical-functions#answer_372726

To walter Roberson sir .... i have a query regarding meijer G function...sir can u please tell me how to simulate the equation of meijer G function in matlab shown in pic ..sir Plz reply

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samriti bali 2019-4-30

Respected sir, i have already gone through this link and all other links....but nothing is clear from it...that's why i posted my query here...if u can tell me the format to write this equation in matlab then ur help will be beneficial for me.

Walter Roberson 2019-5-1

Calculate one term where j=0. The result will be 0 if the term is 0 and otherwise will be infinity times the sign of the term. You have posted an infinite sum whose terms do not vary with the variable of summation so you will either get +inf, 0, or -inf

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