# Confluent hypergeometric function of the first kind Calculator

## Calculates confluent hypergeometric function of the first kind or Kummer's function M(a,b,z).

 $\normal Confluent\ Hypergeometric\ function\ of\ the\ 1st\ kind\\[15]\large \hspace{30} {}_1F_1(a;b;z)=M(a,b,z)\\\hspace{105}=1+\frac{a}{b}z+\frac{a(a+1)}{b(b+1)}\frac{z^2}{2!}+\cdots=\sum_{\small n=0}^{\small \infty}\frac{(a)_n}{(b)_k}\frac{z^n}{n!}\\[10]$
 a b z 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt M(a,b,z)
 $\normal Confluent\ hypergeometric\ differential\ equation\\[15](1)\ zy''+(b-z)y'-ay=0\\\hspace{25} y=c_1M(a,b,z)+c_2U(a,b,z)\\[10](2)\ M(a,b,z)={}_1F_1(a;b;z)\\\hspace{85}=1+{\large\frac{a}{b}}z+{\large\frac{a(a+1)}{b(b+1)}\frac{z^2}{2!}}+\cdots={\large \sum_{\small n=0}^{\small \infty}}{\large \frac{(a)_n}{(b)_k}\frac{z^n}{n!}}\\[10]$

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