Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8j0)

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=3/4

http://functions.wolfram.com/07.23.03.a8j0.01

Input Form

Hypergeometric2F1[-(21/4), 3/4, 5, -z] == (4096 Sqrt[2] (2 (-22848 - 227528 z - 1048747 z^2 - 3148502 z^3 + 5060470 z^4 + 3888128 z^5 + 2232493 z^6 + 859862 z^7 + 197632 z^8 + 20480 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (-22848 - 227528 z - 1048747 z^2 - 3148502 z^3 + 5060470 z^4 + 3888128 z^5 + 2232493 z^6 + 859862 z^7 + 197632 z^8 + 20480 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-45696 - 443632 z - 1991941 z^2 - 5847660 z^3 + 1349450 z^4 + 860276 z^5 + 364947 z^6 + 91456 z^7 + 10240 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-22848 - 227528 z - 1048747 z^2 - 3148502 z^3 + 5060470 z^4 + 3888128 z^5 + 2232493 z^6 + 859862 z^7 + 197632 z^8 + 20480 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (20541646125 Pi z^4 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]