I need to implement the following recursive function in Mathematica.
$$F[-2*a,b,2b;2]=\left(\frac{a-1/2}{a-1/2+b}\right)F\left[-2*(a-1),b,2b;2\right]$$
The conditions of the functions are: if $a=0$, then $F[0,b,2*b,2]=1$, if $a<0$, then $F[-2*a,b,2*b,2]=0$
Is it possible to do it recursively. What I did is:
hyperrec[a_Integer, b_Integer] :=
Simplify[((a - (1/2))/((a - 1/2) + b))*hyperrec[(a - 1), b]]
But I am getting error of hold!
F[-2*a,b,2b;2]
it should be just something likeF[a,b,c,d,....]
etc... I am assuming yourF
function is what you calledhyperrec
in your code. $\endgroup$