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

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=-39/8, b>=a

For fixed z and a=-39/8, b=37/8

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

Input Form

Hypergeometric2F1[-(39/8), 37/8, 21/4, z] == (1/(4444440385 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (444912 + 385020 z + 1051675 z^2 + 4993139 z^3 + 107418441 z^4 - 599861475 z^5 + 1200191520 z^6 - 1172894976 z^7 + 569192448 z^8 - 110297088 z^9 - (1/Sqrt[1 - z]) (444912 + 162564 z + 803551 z^2 + 4391367 z^3 + 104748969 z^4 - 793176535 z^5 + 2126202516 z^6 - 2913292800 z^7 + 2207192064 z^8 - 884539392 z^9 + 147062784 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]