Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8bt)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-9/4

http://functions.wolfram.com/07.23.03.a8bt.01

Input Form

Hypergeometric2F1[-(21/4), -(9/4), 5, z] == (1/(102708230625 Pi z^4)) (4096 (2 (-1152 + 22128 z - 239025 z^2 + 2454450 z^3 + 114730325 z^4 + 218865308 z^5 + 76684553 z^6 + 1018050 z^7 - 58125 z^8 + 2400 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + 4 Sqrt[1 - z] (288 - 5460 z + 58425 z^2 - 599625 z^3 - 16288400 z^4 - 26883742 z^5 - 7962975 z^6 - 3525 z^7 + 150 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-1152 + 22128 z - 239025 z^2 + 2454450 z^3 + 114730325 z^4 + 218865308 z^5 + 76684553 z^6 + 1018050 z^7 - 58125 z^8 + 2400 z^9) 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]