Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bzep)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=3/8, b>=a

For fixed z and a=3/8, b=47/8

http://functions.wolfram.com/07.23.03.bzep.01

Input Form

Hypergeometric2F1[3/8, 47/8, -(21/4), z] == ((1 + Sqrt[1 - z])^(1/4) (-35296352 + 400865712 z - 2096406806 z^2 + 6728527525 z^3 - 15070634655 z^4 + 26715723554 z^5 + 13706257356 z^6 - 5705345943 z^7 + 1735282425 z^8 - 328681360 z^9 + 28842240 z^10 + (1/Sqrt[1 - z]) (2 (-17648176 + 209256944 z - 1146213809 z^2 + 3864414368 z^3 - 9098261455 z^4 + 16763153342 z^5 - 87263603823 z^6 + 34997264148 z^7 - 13745062401 z^8 + 3917769790 z^9 - 697020800 z^10 + 57684480 z^11))))/(70592704 2^(1/4) (-1 + z)^11)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]