Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6k6)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-1/8

http://functions.wolfram.com/07.23.03.b6k6.01

Input Form

Hypergeometric2F1[-(45/8), -(1/8), 19/4, z] == (1/(587189905815 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8592584 + 114047024 z - 787797673 z^2 + 4845673365 z^3 + 44835835214 z^4 - 782764198 z^5 + 283382563 z^6 - 80602511 z^7 + 14773360 z^8 - 1277696 z^9 - (1/Sqrt[1 - z]) (4 (-2148146 + 29585829 z - 210936778 z^2 + 1306463340 z^3 + 1451327959 z^4 - 3284468011 z^5 + 971530948 z^6 - 337635446 z^7 + 90654385 z^8 - 15651776 z^9 + 1277696 z^10))))

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]