Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a850)

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=-21/4

http://functions.wolfram.com/07.23.03.a850.01

Input Form

Hypergeometric2F1[-(21/4), -(21/4), -(1/2), z] == (1/(101640 Pi^(3/2))) ((-4 (-12705 + 698775 z + 11775470 z^2 + 25550070 z^3 + 11505171 z^4 + 814867 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (-12705 + 698775 z + 11775470 z^2 + 25550070 z^3 + 11505171 z^4 + 814867 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (-25410 - 12705 Sqrt[z] + 1397550 z + 4543945 z^(3/2) + 23550940 z^2 + 32987430 z^(5/2) + 51100140 z^3 + 47039010 z^(7/2) + 23010342 z^4 + 15339851 z^(9/2) + 1629734 z^5 + 765765 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-25410 + 12705 Sqrt[z] + 1397550 z - 4543945 z^(3/2) + 23550940 z^2 - 32987430 z^(5/2) + 51100140 z^3 - 47039010 z^(7/2) + 23010342 z^4 - 15339851 z^(9/2) + 1629734 z^5 - 765765 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]