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

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=-25/8, b>=a

For fixed z and a=-25/8, b=43/8

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

Input Form

Hypergeometric2F1[-(25/8), 43/8, -(5/2), -z] == (1/(3648 (1 + z)^(31/8))) ((3648 - 15960 z + 57057 z^2 - 381843 z^3 - 859488 z^4 + 611072 z^5 + 1863680 z^6 + 851968 z^7) Cos[(7 ArcTan[Sqrt[z]])/4] - Sqrt[z] (-6384 + 23541 z - 83391 z^2 + 1043760 z^3 + 3952256 z^4 + 4286464 z^5 + 1490944 z^6) Sin[(7 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]