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

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=-37/8, b>=a

For fixed z and a=-37/8, b=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, 11/4, z] == (1/(57669579 z^2)) (2 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-2 (-5365 - 187775 z + 6771226 z^2 - 39312768 z^3 + 86073856 z^4 - 80740352 z^5 + 27394048 z^6) + (1/Sqrt[1 - z]) (-10730 - 370185 z + 28148963 z^2 - 234110448 z^3 + 743590144 z^4 - 1114685440 z^5 + 796590080 z^6 - 219152384 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]