Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lh)

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=-47/8, b>=a

For fixed z and a=-47/8, b=37/8

http://functions.wolfram.com/07.23.03.b5lh.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(11/2), -z] == (1/(9146368 (1 + z)^(33/8))) ((9146368 - 7743232 z + 10659936 z^2 - 18801483 z^3 + 43238130 z^4 - 148038475 z^5 + 1304015856 z^6 + 9838735104 z^7 + 18386632704 z^8 + 13811646464 z^9 + 3725590528 z^10) Cos[ArcTan[Sqrt[z]]/4] - 4 Sqrt[z] (-571648 + 662592 z - 920199 z^2 + 1541292 z^3 - 3303274 z^4 + 10479469 z^5 + 381982656 z^6 + 921245952 z^7 + 790462464 z^8 + 232849408 z^9) Sin[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]