Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abd9)

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=-15/4, b>=a

For fixed z and a=-15/4, b=3/4

http://functions.wolfram.com/07.23.03.abd9.01

Input Form

Hypergeometric2F1[-(15/4), 3/4, 5, z] == (4096 (-4 (7392 + 7392 Sqrt[z] - 60676 z - 60676 z^(3/2) + 224763 z^2 + 224763 z^(5/2) - 526218 z^3 - 526218 z^(7/2) - 161382 z^4 - 161382 z^(9/2) + 76284 z^5 + 76284 z^(11/2) - 21645 z^6 - 21645 z^(13/2) + 2730 z^7 + 2730 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (29568 - 250096 z + 957649 z^2 - 2313696 z^3 + 2507622 z^4 - 1425372 z^5 + 651105 z^6 - 178620 z^7 + 21840 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(5492021535 Pi Sqrt[1 + Sqrt[z]] z^4)

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]