Please help me in plotting the following functions.

Answer 1

[Torsten]

Limits of Euler's beta function are 0 and 1, not a and b.

So

C_m,i^nu = beta(i*nu+3,(m-i)*nu)/beta(i*nu,(m-i)*nu) + 2

and the beta function is implemented in MATLAB:

https://de.mathworks.com/help/matlab/ref/beta.html

So the infinite series reduces to

S_m^nu = 2 + exp(-m*u) * sum_{i=0}^{oo} beta(i*nu+3,(m-i)*nu)/beta(i*nu,(m-i)*nu) * (m*u)^i / factorial(i)

I think you should be able to take it from here.

[Gufran Malik]

Yes, the limits are 0 and 1. a and b were typed by mistake.