Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a95i)

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=-11/4

http://functions.wolfram.com/07.23.03.a95i.01

Input Form

Hypergeometric2F1[-(19/4), -(11/4), 6, z] == (1/(35242302190095 Pi z^5)) (16384 (-2 Sqrt[1 - z] (-22528 + 412896 z - 3959505 z^2 + 28932134 z^3 - 233549547 z^4 - 3065118768 z^5 - 3663676279 z^6 - 857871330 z^7 - 12917421 z^8 + 282348 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-22528 + 429792 z - 4267593 z^2 + 31873457 z^3 - 254983113 z^4 + 1410167817 z^5 + 7747743197 z^6 + 5829085227 z^7 + 854879157 z^8 + 70587 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-22528 + 412896 z - 3959505 z^2 + 28932134 z^3 - 233549547 z^4 - 3065118768 z^5 - 3663676279 z^6 - 857871330 z^7 - 12917421 z^8 + 282348 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]