Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a89p)

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=-13/4

http://functions.wolfram.com/07.23.03.a89p.01

Input Form

Hypergeometric2F1[-(21/4), -(13/4), 6, -z] == (16384 Sqrt[2] ((-79872 - 1683552 z - 18769413 z^2 - 161050383 z^3 - 1533638925 z^4 + 75906341237 z^5 - 178477215843 z^6 + 102537330003 z^7 - 13754753167 z^8 + 66870375 z^9 + 1244100 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-79872 - 1683552 z - 18769413 z^2 - 161050383 z^3 - 1533638925 z^4 + 75906341237 z^5 - 178477215843 z^6 + 102537330003 z^7 - 13754753167 z^8 + 66870375 z^9 + 1244100 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-79872 - 1663584 z - 18362877 z^2 - 156648765 z^3 - 1496510925 z^4 + 43467452027 z^5 - 90096228671 z^6 + 45897574577 z^7 - 5247302775 z^8 + 311025 z^9) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (-79872 - 1683552 z - 18769413 z^2 - 161050383 z^3 - 1533638925 z^4 + 75906341237 z^5 - 178477215843 z^6 + 102537330003 z^7 - 13754753167 z^8 + 66870375 z^9 + 1244100 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (268664189668875 Pi z^5 Sqrt[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]