I need a method of solution that starts form series of polynomials and convert it to hypergeometric function. i mean how to achieving answer that we already have it. I know that by substituting n in answer the polynomials generated, but this isn't the point that i need it. I'm looking for a...
i want to write a hypergeometric function (2F1(a,b;c,x)) as function of n that generate polynomials below
n=0 → 1
n=1 → y
n=2 → 4(ω+1)y^2-1
n=3 → y(2(2ω+3)y^2-3)
n=4 → 8(ω+2)(2ω+3)y^4-6(6+4ω)y^2+3
... → ...
2F1(a,b;c,x)=1+(ab)/(c)x+(a(a+1)b(b+1))/(c(c+1))x^2/2!+...
the...