Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bja5)

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=27/8

http://functions.wolfram.com/07.23.03.bja5.01

Input Form

Hypergeometric2F1[-(25/8), 27/8, 7/2, -z] == -((64 (Sqrt[z] (2380 - 7735 z - 251398 z^2 - 278931 z^3 + 444640 z^4 + 801024 z^5 + 315392 z^6) Cos[(7 ArcTan[Sqrt[z]])/4] - (1360 - 5355 z + 41650 z^2 + 801409 z^3 + 1979012 z^4 + 1781248 z^5 + 551936 z^6) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (20407387 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]