Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6jt)

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=-1/8

http://functions.wolfram.com/07.23.03.b6jt.01

Input Form

Hypergeometric2F1[-(45/8), -(1/8), 3/2, -z] == -((1/(268345 Sqrt[z] (1 + z)^(3/8))) (4 (4 Sqrt[z] (-19387 + 26450 z + 19204 z^2 + 13814 z^3 + 6815 z^4 + 1984 z^5 + 256 z^6) Cos[(3 ArcTan[Sqrt[z]])/4] - (-13949 + 155804 z + 52530 z^2 + 38764 z^3 + 19619 z^4 + 5840 z^5 + 768 z^6) Sin[(3 ArcTan[Sqrt[z]])/4])))

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]