Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9us)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=21/4

http://functions.wolfram.com/07.23.03.a9us.01

Input Form

Hypergeometric2F1[-(19/4), 21/4, 2, z] == (1/(334639305 Pi z)) (8 (2 Sqrt[1 - z] (-855855 + 157071412 z - 1487671296 z^2 + 4443758592 z^3 - 5226102784 z^4 + 2113929216 z^5) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (855855 (1 + Sqrt[1 - z]) - (74053477 + 157071412 Sqrt[1 - z]) z + 192 (2901315 + 7748288 Sqrt[1 - z]) z^2 - 43008 (32791 + 103324 Sqrt[1 - z]) z^3 + 1835008 (793 + 2848 Sqrt[1 - z]) z^4 - 528482304 (1 + 4 Sqrt[1 - z]) z^5) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

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]