Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7im)

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=-23/8

http://functions.wolfram.com/07.23.03.b7im.01

Input Form

Hypergeometric2F1[-(43/8), -(23/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1847230464 - 37125002880 z + 393324962751 z^2 - 3198481972455 z^3 + 28864470730095 z^4 + 638917617882801 z^5 + 1100324156041765 z^6 + 426002701792419 z^7 + 25495002417885 z^8 - 621076621165 z^9 + 16833245520 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1847230464 - 37817714304 z + 407057425551 z^2 - 3342272696301 z^3 + 30025526783175 z^4 - 552415354837089 z^5 - 2091035045703671 z^6 - 1563014490709191 z^7 - 252756141290739 z^8 - 156058213675 z^9 + 4208311380 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1847230464 - 37125002880 z + 393324962751 z^2 - 3198481972455 z^3 + 28864470730095 z^4 + 638917617882801 z^5 + 1100324156041765 z^6 + 426002701792419 z^7 + 25495002417885 z^8 - 621076621165 z^9 + 16833245520 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (1847230464 - 37125002880 z + 393324962751 z^2 - 3198481972455 z^3 + 28864470730095 z^4 + 638917617882801 z^5 + 1100324156041765 z^6 + 426002701792419 z^7 + 25495002417885 z^8 - 621076621165 z^9 + 16833245520 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (309543990804931407525 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]