Mx (0) is solvable by applying direct elementary substitution.

Similarly, you can differentiate the integral up to any order and then

evaluate at t = 0.

Hi, there is no analytical expression available using MAPLE for example but this certainly comes from some missing assumptions. Is theta positive and lower than one ?

Hi Richard,

Thank you for your answer. θ, λ, α, are positive and greater or equal to zero and t∈(−h,h) for some h>0.

Best wishes

I think , if it is can not solving analytically., we can solve it numerically

Dear Dr, Salah,

It is a Mx(t) so, we need the exact solution to generate rth moment.

Thanks a lot for you.

I wish you all the best

Dear Huda A. Rasheed

I observed that Mx (0) is solvable by direct elementary substitution.

Similarly, you can differentiate the integral up to any order and then

evaluate at t = 0.

Best regards

It seems to me that the leading behaviour of the integrand for large x is exp(0.5ax^2), so I think the integral diverges as it is written. Maybe there is a minus missing in the first exponent? (exp(-x(\lambda -t) - 0.5ax^2)

WE don't see clearly the inyegration

@Huda A. Rasheed

Yeah, for example, there is no analytical expression available using MAPLE because this is probably due to certain expectations that are lacking. Are Theta Negative and Under something?

Dear Abrar,

Thank you for your answer. θ, λ, α, are positive and greater or equal to zero and t∈(−h,h) for some h>0.

Best wishes

السلام عليكم ورحمه الله وبركاته

دكتورة

1- Use binomial expression for the equation

2- Try with transfer gamma or u can use exponential expansion

وعليكم السلام ورحمة الله وبركاته

Thanks a lot, Munder. I will use your suggestion.

I wish you all the best.

Mathematicas

You can use R or Matlap language

Hello Dr. Rasheed

Could you able to solve the integral? I could suggest some references, please check Mathai and Haubold (2008) (Special Function for Applied Scientists, Page 52, example 1.8.3) Provost and Mabrouk (2010) ( https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.621.9888&rep=rep1&type=pdf ).

I hope this will be helpful. With best wishes

Thomas Xavier