Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b76j)

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=39/8

http://functions.wolfram.com/07.23.03.b76j.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, 7/4, z] == (1/(134562351 z)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1046175 - 76469331 z + 694375044 z^2 - 2315016704 z^3 + 3561079808 z^4 - 2577203200 z^5 + 712245248 z^6 + (1/Sqrt[1 - z]) (-1046175 + 144273594 z - 1816186443 z^2 + 8313613616 z^3 - 18320070912 z^4 + 21097922560 z^5 - 12267487232 z^6 + 2848980992 z^7)))

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]