Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bl4u)

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=-21/8, b>=a

For fixed z and a=-21/8, b=-19/8

http://functions.wolfram.com/07.23.03.bl4u.01

Input Form

Hypergeometric2F1[-(21/8), -(19/8), 11/2, z] == (1/(8992509295 z^(9/2))) (1024 (Sqrt[z] (1344 - 18712 z + 134043 z^2 - 742287 z^3 + 14737742 z^4 + 29489034 z^5 + 9507591 z^6 + 368621 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-1792 + 26480 z - 199975 z^2 + 1141574 z^3 - 8781157 z^4 - 16000108 z^5 + 14891519 z^6 + 8554838 z^7 + 368621 z^8) Sin[(3 ArcSin[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]