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

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=13/8

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

Input Form

Hypergeometric2F1[-(21/8), 13/8, 11/2, z] == (1/(117266765 z^(9/2))) (1024 ((-Sqrt[z]) (17472 - 100984 z + 227955 z^2 - 219765 z^3 - 186323 z^4 + 197409 z^5 - 85284 z^6 + 14352 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((-23296 + 154544 z - 418171 z^2 + 548548 z^3 - 146510 z^4 - 275264 z^5 + 238257 z^6 - 92460 z^7 + 14352 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]