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

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=-9/8

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

Input Form

Hypergeometric2F1[-(37/8), -(9/8), 15/4, z] == (1/(8764028445 z^3)) (4 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (390572 - 6402591 z + 78323635 z^2 + 1590243370 z^3 + 1528970306 z^4 - 5877259 z^5 + 769327 z^6 - 57040 z^7 + (1/Sqrt[1 - z]) (-390572 + 6597877 z - 81476109 z^2 - 456353910 z^3 + 316285306 z^4 + 237937369 z^5 - 25605969 z^6 + 3234168 z^7 - 228160 z^8)))

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]