Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7r3)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-43/8, b>=a

For fixed z and a=-43/8, b=7/8

http://functions.wolfram.com/07.23.03.b7r3.01

Input Form

Hypergeometric2F1[-(43/8), 7/8, 6, z] == (1/(60396331901164875 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-562200576 + 5988753792 z - 29098872495 z^2 + 85844174493 z^3 - 177092357904 z^4 - 71736451590 z^5 + 51999757505 z^6 - 27134107575 z^7 + 9487987470 z^8 - 1990007760 z^9 + 189352800 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (35137536 - 348767496 z + 1567755189 z^2 - 4249565859 z^3 - 30318992550 z^4 + 22801252890 z^5 - 12344055215 z^6 + 4466163585 z^7 - 966600960 z^8 + 94676400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (70275072 - 737064720 z + 3519947277 z^2 - 10188049641 z^3 + 66701783610 z^4 - 49397004210 z^5 + 31774418225 z^6 - 14745441045 z^7 + 4621719960 z^8 - 875531280 z^9 + 75741120 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-562200576 + 5988753792 z - 29098872495 z^2 + 85844174493 z^3 - 177092357904 z^4 - 71736451590 z^5 + 51999757505 z^6 - 27134107575 z^7 + 9487987470 z^8 - 1990007760 z^9 + 189352800 z^10) EllipticK[1/2 - 1/(Sqrt[2] 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]