Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bbh4)

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.bbh4.01

Input Form

Hypergeometric2F1[-(37/8), -(9/8), 23/4, z] == (1/(1452522398595 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1321936 - 19498556 z + 145315317 z^2 - 793172330 z^3 + 4839361979 z^4 + 61056648792 z^5 + 39170569723 z^6 - 92691426 z^7 + 9215525 z^8 - 536176 z^9 + (1/Sqrt[1 - z]) (-1321936 + 20159524 z - 154899353 z^2 + 863475290 z^3 - 5218950751 z^4 - 13336432696 z^5 + 13133782553 z^6 + 5053927954 z^7 - 395932465 z^8 + 38336584 z^9 - 2144704 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]