Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9yb)

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=-9/2, b>=a

For fixed z and a=-9/2, b=-17/4

http://functions.wolfram.com/07.23.03.a9yb.01

Input Form

Hypergeometric2F1[-(9/2), -(17/4), 6, z] == (16 Sqrt[2] (2 (65536 - 1431552 z + 16650880 z^2 - 150473344 z^3 + 1530648000 z^4 + 63498380192 z^5 + 159033518536 z^6 + 104317115760 z^7 + 18945321142 z^8 + 653882185 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (65536 - 1431552 z + 16650880 z^2 - 150473344 z^3 + 1530648000 z^4 + 63498380192 z^5 + 159033518536 z^6 + 104317115760 z^7 + 18945321142 z^8 + 653882185 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (65536 - 1398784 z + 15961728 z^2 - 142705920 z^3 + 1461682880 z^4 + 28431406432 z^5 + 54956852872 z^6 + 27618242696 z^7 + 3542573430 z^8 + 65211575 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (65536 - 1431552 z + 16650880 z^2 - 150473344 z^3 + 1530648000 z^4 + 63498380192 z^5 + 159033518536 z^6 + 104317115760 z^7 + 18945321142 z^8 + 653882185 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (65536 - 1431552 z + 16650880 z^2 - 150473344 z^3 + 1530648000 z^4 + 63498380192 z^5 + 159033518536 z^6 + 104317115760 z^7 + 18945321142 z^8 + 653882185 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (65536 - 1431552 z + 16650880 z^2 - 150473344 z^3 + 1530648000 z^4 + 63498380192 z^5 + 159033518536 z^6 + 104317115760 z^7 + 18945321142 z^8 + 653882185 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (286213602675 Pi Sqrt[1 + Sqrt[1 - z]] z^5)

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]