hypergeometrics.Rd
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) .
hypergeometric0F1(a, z) hypergeometric1F1(a, b, z) hypergeometric2F1(a, b, c, z)
a | the first parameter; |
---|---|
z | the argument raised to the powers 0 ... infinity ; |
b | the second parameter; |
c | the third parameter; |
The result of the hypergeometric function.
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.
hypergeometric0F1(12, 0.4) # 1.033851 #> [1] 1.033851 hypergeometric1F1(12, 14, 0.4) # 1.409877 #> [1] 1.409877 hypergeometric2F1(12, 14, 16, 0.4) # 205.5699 #> [1] 205.5699