# 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 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit M(a,b,z)
 $\normal Confluent\ hypergeometric\ differential\ equation\\[15](1)\ zy''+(b-z)y'-ay=0\\\hspace{25} y=c_1M(a,b,z)+c_2U(a,b,z)\\[10](2)\ M(a,b,z)={}_1F_1(a;b;z)\\\hspace{85}=1+{\large\frac{a}{b}}z+{\large\frac{a(a+1)}{b(b+1)}\frac{z^2}{2!}}+\cdots={\large \sum_{\small n=0}^{\small \infty}}{\large \frac{(a)_n}{(b)_k}\frac{z^n}{n!}}\\[10]$
Confluent hypergeometric function of the first kind
 [1-4] /4 Disp-Num5103050100200
[1]  2018/09/26 05:35   Female / 50 years old level / A teacher / A researcher / Very /
Purpose of use
verified a 3rd-party programmed function, which exploded at larger z. You have a much better solution. thank you!
Comment/Request
You have a much better solution. thank you!
[2]  2018/02/23 22:19   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
verifying values from scipy
[3]  2015/03/30 05:40   Male / 40 years old level / Self-employed people / Useful /
Purpose of use
Test my routines for confluent function calculations
[4]  2014/05/13 20:09   Female / 60 years old level or over / A teacher / A researcher / A little /
Purpose of use
self-education - (re)learning quantum mechanics.
Comment/Request
possibility to graph function on an appropriate domain, and especially see graphs of combined functions containing 1F1 and others would be very useful.

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