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

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=-1/8

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

Input Form

Hypergeometric2F1[-(37/8), -(1/8), 19/4, z] == (1/(352313943489 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-2148146 + 25484823 z - 155112880 z^2 + 824943860 z^3 + 6541598602 z^4 - 84462693 z^5 + 22964304 z^6 - 4356430 z^7 + 399280 z^8) + (1/Sqrt[1 - z]) (8592584 - 106235584 z + 670347093 z^2 - 3597795825 z^3 - 2568406102 z^4 + 6844924062 z^5 - 1598545287 z^6 + 414825539 z^7 - 74094960 z^8 + 6388480 z^9)))

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]