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

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=-13/8, b>=a

For fixed z and a=-13/8, b=45/8

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

Input Form

Hypergeometric2F1[-(13/8), 45/8, -(11/2), z] == -((1/(338415616 (1 - z)^(19/2))) (Sqrt[1 - z] (-338415616 + 2578496256 z - 8051070944 z^2 + 12468464943 z^3 - 7904486268 z^4 - 2024319654 z^5 - 3448840892 z^6 + 11728900623 z^7 - 12696442336 z^8 + 7176795616 z^9 - 2150362368 z^10 + 271510400 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + 4 Sqrt[z] (-63452928 + 492721600 z - 1574298089 z^2 + 2518043436 z^3 - 1713709760 z^4 - 299899208 z^5 - 2024552805 z^6 + 4325953528 z^7 - 4008253562 z^8 + 2054509500 z^9 - 571529392 z^10 + 67877600 z^11) 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]