equation 7.4.10 from handbook of mathematical functions

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);

[Walter Roberson]

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.

Answer 1

[Birdman]

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

[Tammun filistin]

Thank you :)

Answer 2

[Star Strider]

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

[Tammun filistin]

Many thanks

Answer 3

[samriti bali]

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

[Walter Roberson]

https://www.mathworks.com/help/symbolic/meijerg.html

[samriti bali]

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]

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