# Confluent hypergeometric function of the second kind Calculator

## Calculates confluent hypergeometric function of the second kind or Tricomi's function U(a,b,z).

 $\normal Confluent\ Hypergeometric\ function\ of\ the\ 2nd\ kind\\[15]\hspace{30} U(a,b,z)=\frac{\Gamma(1-b)}{\Gamma(a-b+1)}M(a,b,z)+\frac{\Gamma(b-1)}{\Gamma(a)}z^{1-b}M(a-b+1,2-b,z)\\[10]$

 a b z 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit U(a,b,z)
 $\normal Confluent\ hypergeometric\ differential\ equation\\[15](1)\ zy''+(b-z)y'-ay=0\\\hspace{25} y=c_1M(a,b,z)+c_2U(a,b,z)\\[10]$

Confluent hypergeometric function of the second kind
 [1-2] /2 Disp-Num5103050100200
[1]  2014/07/19 07:29   Male / 50 years old level / An engineer / Not at All /
Purpose of use
Confirmation of my own implementation.
Comment/Request
Are the results of Kummer U correct for larges values of a? For instance, when a=50, b= 0.2, z = 5, the output is -6.E-73. In fact the results are negative for many cases.
[2]  2013/03/15 10:28   Male / 30 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Working on a thesis.
Comment/Request
How do I compute the U(a,b,z) when a=-2500,b=0.5,large z for example z=10268.
from Keisan
Confluent hypergeometric function of the second kind:
U(-2500,0.5,10268)= 5.71332832943457105E+9632
This answer is the same as KummerU(-2500,0.5,10268) in Maple9.5.

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