# relation to Kummer equation

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##### 1: 13.14 Definitions and Basic Properties
###### Whittaker’s Equation
Standard solutions are: …
##### 3: 6.11 Relations to Other Functions
6.11.3 $\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)=U\left(1,1,-iz\right).$
##### 5: 13.3 Recurrence Relations and Derivatives
###### §13.3(i) Recurrence Relations
Kummer’s differential equation (13.2.1) is equivalent to
##### 7: 7.11 Relations to Other Functions
###### Confluent Hypergeometric Functions
7.11.4 $\operatorname{erf}z=\frac{2z}{\sqrt{\pi}}M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{% 2}\right)=\frac{2z}{\sqrt{\pi}}e^{-z^{2}}M\left(1,\tfrac{3}{2},z^{2}\right),$
##### 8: 8.19 Generalized Exponential Integral
###### §8.19(i) Definition and Integral Representations
In Figures 8.19.28.19.5, height corresponds to the absolute value of the function and color to the phase. …
###### §8.19(vi) Relationto Confluent Hypergeometric Function
For $U\left(a,b,z\right)$ see §13.2(i). …
##### 10: 18.11 Relations to Other Functions
###### §18.11 Relationsto Other Functions
See §§18.5(i) and 18.5(iii) for relations to trigonometric functions, the hypergeometric function, and generalized hypergeometric functions.