Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bck0)

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=-15/8

http://functions.wolfram.com/07.23.03.bck0.01

Input Form

Hypergeometric2F1[-(35/8), -(15/8), 5/2, -z] == -((1/(435643 z^(3/2) (1 + z)^(5/8))) (16 (Sqrt[z] (-175 - 34173 z + 173730 z^2 - 144690 z^3 + 13405 z^4 + 815 z^5 + 48 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - 2 (-70 - 2765 z + 49590 z^2 - 98430 z^3 + 32298 z^4 + 515 z^5 + 30 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]