Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bz6v)

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=3/8, b>=a

For fixed z and a=3/8, b=37/8

http://functions.wolfram.com/07.23.03.bz6v.01

Input Form

Hypergeometric2F1[3/8, 37/8, -(11/2), z] == (1/(9146368 (1 - z)^(21/2))) (Sqrt[1 - z] (9146368 - 96920320 z + 468705888 z^2 - 1373200431 z^3 + 2746280715 z^4 - 4115754762 z^5 + 6190487030 z^6 - 1360982243 z^7 + 395999487 z^8 - 76539124 z^9 + 6970288 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (6859776 - 73690624 z + 361504836 z^2 - 1074985659 z^3 + 2182248695 z^4 - 3312829674 z^5 + 6825989634 z^6 - 1549850239 z^7 + 433397763 z^8 - 80024268 z^9 + 6970288 z^10) 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]