Hypergeometric Function

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

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The geometric series ?? I get the series of [itex] e^{x} [/itex].

Daniel.
 
The geometric series ?? I get the series of [itex] e^{x} [/itex].

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

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

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

which converges for |x|<1 to [itex] \frac{1}{1-x} [/itex]

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

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

which converges for |x|<1 to [itex] \frac{1}{1-x} [/itex]

Daniel.
Cheers thanks
 
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


[tex]
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}]
[/tex]

Now I need to find


[tex]
F(a, a+\frac{1}{2}, \frac{5}{2}, z^2)
[/tex]


[tex]
F(a, a+\frac{1}{2}, \frac{7}{2}, z^2)
[/tex]


and, it would be great if I find

[tex]
F(a, a+\frac{1}{2}, n+ \frac{1}{2}, z^2)
[/tex]


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

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