# relations to confluent hypergeometric functions and generalized hypergeometric functions

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##### 1: 7.11 Relations to Other Functions
###### ConfluentHypergeometricFunctions
7.11.4 $\operatorname{erf}z=\frac{2z}{\sqrt{\pi}}M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{% 2}\right)=\frac{2z}{\sqrt{\pi}}e^{-z^{2}}M\left(1,\tfrac{3}{2},z^{2}\right),$
##### 2: 16.25 Methods of Computation
###### §16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. They are similar to those described for confluent hypergeometric functions, and hypergeometric functions in §§13.29 and 15.19. There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …Instead a boundary-value problem needs to be formulated and solved. …
##### 3: 10.39 Relations to Other Functions
###### ConfluentHypergeometricFunctions
For the functions $M$, $U$, $M_{0,\nu}$, and $W_{0,\nu}$ see §§13.2(i) and 13.14(i).
##### 4: 10.16 Relations to Other Functions
###### ConfluentHypergeometricFunctions
For the functions $M$ and $U$ see §13.2(i). …
##### 6: 18.34 Bessel Polynomials
###### §18.34(i) Definitions and Recurrence Relation
18.34.1 $y_{n}\left(x;a\right)={{}_{2}F_{0}}\left({-n,n+a-1\atop-};-\frac{x}{2}\right)=% {\left(n+a-1\right)_{n}}\left(\frac{x}{2}\right)^{n}{{}_{1}F_{1}}\left({-n% \atop-2n-a+2};\frac{2}{x}\right).$
##### 8: 16.18 Special Cases
###### §16.18 Special Cases
The ${{}_{1}F_{1}}$ and ${{}_{2}F_{1}}$ functions introduced in Chapters 13 and 15, as well as the more general ${{}_{p}F_{q}}$ functions introduced in the present chapter, are all special cases of the Meijer $G$-function. This is a consequence of the following relations: …As a corollary, special cases of the ${{}_{1}F_{1}}$ and ${{}_{2}F_{1}}$ functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer $G$-function. …