Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7c2)

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=-45/8, b>=a

For fixed z and a=-45/8, b=47/8

http://functions.wolfram.com/07.23.03.b7c2.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, 7/2, -z] == (64 (4 Sqrt[z] (3219 - 59015 z + 8020402 z^2 + 99122478 z^3 + 428759760 z^4 + 897841152 z^5 + 990167040 z^6 + 554827776 z^7 + 124780544 z^8) Cos[(3 ArcTan[Sqrt[z]])/4] - (17168 - 312243 z + 9753570 z^2 + 197100189 z^3 + 1014984880 z^4 + 2340658944 z^5 + 2748235776 z^6 + 1609891840 z^7 + 374341632 z^8) Sin[(3 ArcTan[Sqrt[z]])/4]))/(1582820785 z^(5/2) (1 + z)^(3/8))

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]