Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3ub)

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=11/8, b>=a

For fixed z and a=11/8, b=45/8

http://functions.wolfram.com/07.23.03.c3ub.01

Input Form

Hypergeometric2F1[11/8, 45/8, -(7/2), z] == (1/(1922816 (1 - z)^(21/2))) (Sqrt[1 - z] (1922816 - 24018032 z + 148836903 z^2 - 670362115 z^3 + 3890022010 z^4 + 5477478474 z^5 - 534051973 z^6 + 108331081 z^7 - 16915212 z^8 + 1334736 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (1442112 - 18223832 z + 114123207 z^2 - 517502535 z^3 + 6350777026 z^4 + 5731968138 z^5 - 586186533 z^6 + 116621845 z^7 - 17582580 z^8 + 1334736 z^9) 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]