hypergeometrics {CohensdpLibrary} R Documentation

## hypergeometric functions.

### Description

The hypergeometric functions are a series of functions which includes the hypergeometric0F1, called the confluent hypergeometric limit function (D. Cousineau); the hypergeometric1F1, called the confluent hypergeometric function (Moreau 2014); and the hypergeometric2F1, called Gauss' confluent hypergeometric function (Michel and Stoitsov 2008). These functions are involved in the computation of the K' and Lambda' distributions, as well as the Chi-square" and the t" distributions (Cousineau 2022).

### Usage

hypergeometric0F1(a, z)
hypergeometric1F1(a, b, z)
hypergeometric2F1(a, b, c, z)


### Arguments

 a the first parameter; z the argument raised to the powers 0 ... infinity ; b the second parameter; c the third parameter;

### Value

The result of the hypergeometric function.


### References

Cousineau D (2022). “The exact distribution of the Cohen's d_p in repeated-measure designs.” doi:10.31234/osf.io/akcnd, https://psyarxiv.com/akcnd/.

Michel N, Stoitsov MV (2008). “Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions.” Computer Physics Communications, 178(7), 535-551. doi:10.1016/j.cpc.2007.11.007.

Moreau J (2014). “Fortran Routines for Computation of Special Functions.” http://jean-pierre.moreau.pagesperso-orange.fr/fortran.html.

### Examples


hypergeometric0F1(12, 0.4)         #   1.033851
hypergeometric1F1(12, 14, 0.4)     #   1.409877
hypergeometric2F1(12, 14, 16, 0.4) # 205.5699



[Package CohensdpLibrary version 0.5.10 Index]