Hypergeometric Function in Matlab

Can somebody help me to write the hypergeometric fucntion in code form?

[KSSV]

Where is the formula for F0?

[AVM]

I think matlab has in-build hypergeometric fucntion and I have to call that which is one of the standard generalized hypergeometric fucntion of this order .

Answer 1

[David Goodmanson]

Hello PM,

The variable l does not come out so well in this font so I'll call it q instead. SInce both -q and -n are negative, the series terminates and is a polynomial. The function 2F0(z) is defined as

Sum{j}  (gamma(j-q)*gamma(j-n) / ( gamma(-q)*gamma(-n)*j! ) *z^j

and with the important identity

gamma(j-q) / gamma(-q) = q! / (q-j)! * (-)^j   [using ! does something funky to the type color]

you can arrive at

Sum{j}  (factorial(q)*factorial(n))  /  (factorial(q-j)*factorial(n-j)*factorial(j)) * (1/c).^j

The last term in the series occurs when either q-j is zero or n-j is zero, whichever comes first. So you can put this expression into a for loop in j, which runs from j = 0 to j = min(q,n).

[AVM]

@David: Thanks for your information.