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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, 9/4, z] == (1/(183230845 z^2)) (2 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (243846 + 26091522 z - 462009316 z^2 + 2218052352 z^3 - 4411438080 z^4 + 3899392000 z^5 - 1270087680 z^6 + (1/Sqrt[1 - z]) (-243846 - 25969599 z + 520893269 z^2 - 3018376720 z^3 + 7837765376 z^4 - 10266296320 z^5 + 6645678080 z^6 - 1693450240 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]