Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b668)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-41/8

http://functions.wolfram.com/07.23.03.b668.01

Input Form

Hypergeometric2F1[-(45/8), -(41/8), 11/2, -z] == (1024 (Sqrt[z] (960 + 26680 z + 419373 z^2 + 5771160 z^3 + 1043794492 z^4 - 6562018632 z^5 + 11576584350 z^6 - 7281622104 z^7 + 1617621660 z^8 - 102677424 z^9 + 817949 z^10) Cos[(3 ArcTan[Sqrt[z]])/4] - (1280 + 35760 z + 564309 z^2 + 7775256 z^3 + 182997180 z^4 - 3175722264 z^5 + 9979102510 z^6 - 10409438232 z^7 + 3937382172 z^8 - 488969240 z^9 + 13392933 z^10) Sin[(3 ArcTan[Sqrt[z]])/4]))/ (929151620397 z^(9/2) (1 + z)^(3/8))

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]