- #1
matematikuvol
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Hypergeometric function is defined by:
[tex]_2F_1(a,b,c,x)=\sum^{\infty}_{n=0}\frac{(a)_n(b)_n}{n!(c)_n}x^n[/tex]
where ##(a)_n=a(a+1)...(a+n-1)##...
I'm confused about this notation in case, for example, ##_2F_1(-n,b,b,1-x)##.
Is that
[tex]_2F_1(-n,b,b,1-x)=\sum^{\infty}_{n=0}\frac{(-n)_n}{n!}(1-x)^n[/tex]
or
[tex]_2F_1(-n,b,b,1-x)=\sum^{\infty}_{k=0}\frac{(-n)_k}{k!}(1-x)^k[/tex]
and how to summate ##_2F_1(-n,b,b,1-x)##?
And one more question. Are the generalised hypergeometric function and confluent hypergeometric function same function?
[tex]_2F_1(a,b,c,x)=\sum^{\infty}_{n=0}\frac{(a)_n(b)_n}{n!(c)_n}x^n[/tex]
where ##(a)_n=a(a+1)...(a+n-1)##...
I'm confused about this notation in case, for example, ##_2F_1(-n,b,b,1-x)##.
Is that
[tex]_2F_1(-n,b,b,1-x)=\sum^{\infty}_{n=0}\frac{(-n)_n}{n!}(1-x)^n[/tex]
or
[tex]_2F_1(-n,b,b,1-x)=\sum^{\infty}_{k=0}\frac{(-n)_k}{k!}(1-x)^k[/tex]
and how to summate ##_2F_1(-n,b,b,1-x)##?
And one more question. Are the generalised hypergeometric function and confluent hypergeometric function same function?
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