Triple integral found sym ?

I am trying to perform a numerical triple integral over s, gamma1, gamma2. The limits are (-inf +int) (0,+inf) and (gamma1,+inf) respectively.

The following is my code

syms s
syms gamma1
syms gamma2

fun=-(exp(-(28035689158432973*pi*gamma2^(2/3))/2305843009213693952)*exp(-(pi*s*7120816246010697*i)/112589990684262400)*(1/((pi*s*(4194304/gamma1^2 + 4194304/gamma2^2)*i)/(50*(6144/gamma1 + 6144/gamma2)) + 1)^((3*(2048/gamma1 + 2048/gamma2)^2)/(4194304/gamma1^2 + 4194304/gamma2^2)) - 1)*(exp(-(pi^2*s*(log((-(gamma2*25*i)/(1024*pi*s))^(1/3) + 1)/3; 

y=@(s,gamma1,gamma2)fun;
gamma2min=@(s,gamma1) gamma1;
prob=integral3(y,-inf,+inf,0,+inf,gamma2min,+inf)

I get the following error

Error using integralCalc/finalInputChecks (line 511) Input function must return 'double' or 'single' values. Found 'sym'.

Any advice?

Thank you very much!

Answer 1

[Roger Stafford]

Matlab's error message has told you what one difficulty is. Your input function is returning 'sym' values because you declared s, gamma1, and gamma2 as of type 'sym', and 'integral' expects a numeric type, 'double' or 'single'. You should eliminate the 'syms' declarations.

Also I notice that there are fractional powers of quantities such as

   (-(gamma2*25*i)/(1024*pi*s))^(1/3)

where the 1/3 power can yield any one of three possible results. You need to resolve any such ambiguities, or you may get results other than what you expect.

[DM]

Thanks, what are the three possible results, you mentioned?

Answer 2

[MA]

fist of all your function hasn't written correct syntactically, then you can use this code:

syms s gamma1 gamma2
y=f(s,gamma1,gamma2);
prob=double(int(int(int(y,gamma2,gamma1,+inf),gamma1,0,+inf),s,-inf,+inf))

[DM]

The function is not integrable symbollically, this is why I chose to do it numerically. I dont think I can use the int function as you provided.