Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b70r)

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=31/8

http://functions.wolfram.com/07.23.03.b70r.01

Input Form

Hypergeometric2F1[-(45/8), 31/8, -(17/4), z] == (1/(12512 2^(1/4) (-1 + z)^2)) ((1 + Sqrt[1 - z])^(1/4) (6256 + 19964 z + 54763 z^2 + 164565 z^3 + 688160 z^4 - 14302464 z^5 + 25636864 z^6 - 12255232 z^7 + (1/Sqrt[1 - z]) (6256 + 16836 z + 43999 z^2 + 134297 z^3 + 597540 z^4 + 35611136 z^5 - 123689984 z^6 + 136249344 z^7 - 49020928 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]