Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5cy)

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=-47/8, b>=a

For fixed z and a=-47/8, b=21/8

http://functions.wolfram.com/07.23.03.b5cy.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1098088448 + 6730081152 z - 13951400053 z^2 + 4958689692 z^3 + 11472222762 z^4 - 59656091396 z^5 + 98805713699 z^6 - 88858771056 z^7 + 46708911744 z^8 - 13574178816 z^9 + 1695006720 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1098088448 + 6730081152 z - 13951400053 z^2 + 4958689692 z^3 + 11472222762 z^4 - 59656091396 z^5 + 98805713699 z^6 - 88858771056 z^7 + 46708911744 z^8 - 13574178816 z^9 + 1695006720 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1098088448 + 6730081152 z - 13951400053 z^2 + 4958689692 z^3 + 11472222762 z^4 - 59656091396 z^5 + 98805713699 z^6 - 88858771056 z^7 + 46708911744 z^8 - 13574178816 z^9 + 1695006720 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-1098088448 + 7141864320 z - 16362583525 z^2 + 9560185635 z^3 + 10715812470 z^4 + 131841780862 z^5 - 398382571345 z^6 + 548295953535 z^7 - 439542950880 z^8 + 212131856640 z^9 - 57545478144 z^10 + 6780026880 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (51317288733966255 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]