hypergeometrics {CohensdpLibrary} | R Documentation |
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
hypergeometric1F1(12, 14, 0.4) # 1.409877
hypergeometric2F1(12, 14, 16, 0.4) # 205.5699