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

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=35/8

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

Input Form

Hypergeometric2F1[-(25/8), 35/8, 7/2, -z] == -((64 (4 Sqrt[z] (595 - 4165 z - 251982 z^2 - 476604 z^3 + 385760 z^4 + 1199616 z^5 + 585728 z^6) Cos[(7 ArcTan[Sqrt[z]])/4] - (1360 - 10455 z + 133450 z^2 + 3259449 z^3 + 10235232 z^4 + 11216128 z^5 + 4100096 z^6) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (78714207 z^(5/2) (1 + z)^(7/8)))

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]