Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9y9)

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.a9y9.01

Input Form

Hypergeometric2F1[-(9/2), -(17/4), 4, z] == (Sqrt[2] (2 (17408 - 471104 z + 9555360 z^2 + 697804800 z^3 + 2616703200 z^4 + 2396213676 z^5 + 578945702 z^6 + 25661455 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (17408 - 471104 z + 9555360 z^2 + 697804800 z^3 + 2616703200 z^4 + 2396213676 z^5 + 578945702 z^6 + 25661455 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (17408 - 462400 z + 9326880 z^2 + 332277600 z^3 + 968364000 z^4 + 680061996 z^5 + 115834190 z^6 + 2723825 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (17408 - 471104 z + 9555360 z^2 + 697804800 z^3 + 2616703200 z^4 + 2396213676 z^5 + 578945702 z^6 + 25661455 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (17408 - 471104 z + 9555360 z^2 + 697804800 z^3 + 2616703200 z^4 + 2396213676 z^5 + 578945702 z^6 + 25661455 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (17408 - 471104 z + 9555360 z^2 + 697804800 z^3 + 2616703200 z^4 + 2396213676 z^5 + 578945702 z^6 + 25661455 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (185059875 Pi Sqrt[1 + Sqrt[1 - z]] z^3)

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]