Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c0d0)

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=5/8, b>=a

For fixed z and a=5/8, b=41/8

http://functions.wolfram.com/07.23.03.c0d0.01

Input Form

Hypergeometric2F1[5/8, 41/8, -(23/4), z] == (-1538240 + 17873680 z - 96004920 z^2 + 317875965 z^3 - 736473905 z^4 + 1326092730 z^5 - 2392860250 z^6 - 313897119 z^7 + 78199155 z^8 - 13353048 z^9 + 1098048 z^10 + (1/Sqrt[1 - z]) (-1538240 + 18642800 z - 104749480 z^2 + 363740355 z^3 - 884468290 z^4 + 1659939365 z^5 - 2980421620 z^6 - 6492407331 z^7 + 1466428398 z^8 - 349157205 z^9 + 56431824 z^10 - 4392192 z^11))/(1538240 2^(3/4) (1 + Sqrt[1 - z])^(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]