- #1

matematikuvol

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## Homework Statement

Calculate

[tex]_2F_1(\frac{1}{2},\frac{1}{2},\frac{3}{2};x)[/tex]

## Homework Equations

[tex]_2F_1(a,b,c;x)=\sum^{\infty}_{n=0}\frac{(a)_n(b)_n}{n!(c)_n}x^n[/tex]

[tex](a)_n=a(a+1)...(a+n-1)[/tex]

## The Attempt at a Solution

[tex](\frac{1}{2})_n=\frac{1}{2}\frac{3}{2}\frac{5}{2}...\frac{2n-1}{2}[/tex]

[tex](\frac{3}{2})_n=\frac{3}{2}\frac{5}{2}\frac{7}{2}...\frac{2n+1}{2}[/tex]

From this relations

[tex]\frac{(\frac{1}{2})_n}{(\frac{3}{2})_n}=\frac{1}{2n+1}[/tex]

But I don't see how to calculate this to the end...