View source for Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m

==Theorem==
The following formula holds:
$$\displaystyle\lim_{c \rightarrow -m} \dfrac{1}{\Gamma(c)} {}_2F_1(a,b;c;z)= \dfrac{(a)_{m+1} (b)_{m+1}}{(m+1)!} z^{m+1} {}_2F_1 \left( a+m+1, b+m+1; m+2; z \right),$$
where $\Gamma$ denotes the [[gamma]] function, $(a)_{m+1}$ denotes the [[Pochhammer]] symbol, and ${}_2F_1$ denotes the [[hypergeometric 2F1]].

==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Hypergeometric 2F1|next=2F1(1,1;2;z)=-log(1-z)/z}}: 15.1.2

[[Category:Theorem]]
[[Category:Unproven]]