Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd5k)

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=-35/8, b>=a

For fixed z and a=-35/8, b=33/8

http://functions.wolfram.com/07.23.03.bd5k.01

Input Form

Hypergeometric2F1[-(35/8), 33/8, 5/2, -z] == -((1/(2848435 z^(3/2) (1 + z)^(5/8))) (16 (Sqrt[z] (-3135 - 81430 z + 454513 z^2 + 3880352 z^3 + 8259328 z^4 + 7073792 z^5 + 2162688 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - 4 (-627 + 19437 z + 394358 z^2 + 1711372 z^3 + 2998688 z^4 + 2337280 z^5 + 675840 z^6) Sin[(5 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]