Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c1e9)

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=7/8, b>=a

For fixed z and a=7/8, b=43/8

http://functions.wolfram.com/07.23.03.c1e9.01

Input Form

Hypergeometric2F1[7/8, 43/8, -(21/4), z] == (-426816 + 5157360 z - 29147976 z^2 + 103572819 z^3 - 267707055 z^4 + 596078070 z^5 - 2660969190 z^6 - 96114865 z^7 + 21799085 z^8 - 3501400 z^9 + 275520 z^10 + (1/Sqrt[1 - z]) (-426816 + 5370768 z - 31673304 z^2 + 117528813 z^3 - 316155630 z^4 + 718616955 z^5 - 2931011820 z^6 - 794632685 z^7 + 152830370 z^8 - 33040875 z^9 + 4982320 z^10 - 367360 z^11))/(426816 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-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]