Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b75q)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b75q.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, -(21/4), z] == (1/(5430208 2^(1/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(1/4) (2715104 + 3490848 z + 5174954 z^2 + 9200552 z^3 + 21385722 z^4 + 79277044 z^5 - 1718483712 z^6 + 3898819584 z^7 - 3235381248 z^8 + 931397632 z^9 + (1/Sqrt[1 - z]) (2715104 + 2133296 z + 3090142 z^2 + 6007025 z^3 + 15814340 z^4 + 66900077 z^5 + 4184699376 z^6 - 16681429248 z^7 + 24186961920 z^8 - 15502868480 z^9 + 3725590528 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]