Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4u9)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-19/8

http://functions.wolfram.com/07.23.03.b4u9.01

Input Form

Hypergeometric2F1[-(47/8), -(19/8), 21/4, z] == (1/(16888979789325 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (6970288 - 145169652 z + 1667540871 z^2 - 16743804661 z^3 + 427705886139 z^4 + 2006008078599 z^5 + 1831703298869 z^6 + 346203292113 z^7 - 4792180023 z^8 + 323755217 z^9 - 13648560 z^10 + (1/Sqrt[1 - z]) (-6970288 + 148654796 z - 1739254411 z^2 + 17559864533 z^3 - 435878146687 z^4 - 1266368751487 z^5 + 461550012423 z^6 + 1091309339487 z^7 + 139753918299 z^8 - 6757686401 z^9 + 447217816 z^10 - 18198080 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]