Hypergeometric Function

[Gypsumfantastic]

How would i go about showing the special case F(1, b, b; x) of the hypergeometic function is the geometric series and also how the geometric series is = 1/ (1 -x)


Cheers,

Dave

[dextercioby]

The geometric series ?? I get the series of e^{x} .

Daniel.

[Gypsumfantastic]

The geometric series ?? I get the series of e^{x} .

Daniel.


I checked it on mathworld that one of the special cases off the hypergeometric function is F(1,1,1;x) is 1 / (1-x) and i want to know how to show it one of my questions is also show that F(1, b, b;x) is the sum to infinity of x^n

[dextercioby]

Ok, my mistake. The factorial in the denominator simplifies through. So

_{2}F_{1}\left(1,b;b;x\right)=\sum_{\nu=0}^{\infty } x^{\nu}

which converges for |x|<1 to \frac{1}{1-x}

Daniel.

[Gypsumfantastic]

Ok, my mistake. The factorial in the denominator simplifies through. So

_{2}F_{1}\left(1,b;b;x\right)=\sum_{\nu=0}^{\infty } x^{\nu}

which converges for |x|<1 to \frac{1}{1-x}

Daniel.

Cheers thanks

[VatanparvaR]

Sorry in advance that I'm posting the same thing in two threads.
I really need it !!!


From Abramowitz's book I got this one



F(a, a+\frac{1}{2}, \frac{3}{2}, z^2)=\frac{1}{2}z^{-1}(1-2a)^{-1}[(1+z)^{1-2a}-(1-z)^{1-2a}]


Now I need to find



F(a, a+\frac{1}{2}, \frac{5}{2}, z^2)




F(a, a+\frac{1}{2}, \frac{7}{2}, z^2)



and, it would be great if I find


F(a, a+\frac{1}{2}, n+ \frac{1}{2}, z^2)



are there any books, handbooks, or websites that I could find this guy?