Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb8a)

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=-33/8

http://functions.wolfram.com/07.23.03.bb8a.01

Input Form

Hypergeometric2F1[-(37/8), -(33/8), 23/4, z] == (1/(3639850245891 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (188848 - 4201868 z + 50502891 z^2 - 488306205 z^3 + 6087385447 z^4 + 183496601655 z^5 + 471248805921 z^6 + 327690599241 z^7 + 65056422045 z^8 + 2618650473 z^9 + (1/Sqrt[1 - z]) (-188848 + 4296292 z - 52580219 z^2 + 513044220 z^3 - 6325480928 z^4 - 66765629564 z^5 - 51132262686 z^6 + 67920271092 z^7 + 49642648440 z^8 + 6117365928 z^9 + 78516273 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]