Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9n6)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-37/8

http://functions.wolfram.com/07.23.03.b9n6.01

Input Form

Hypergeometric2F1[-(39/8), -(37/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (14169505792 - 328942862976 z + 4117225185801 z^2 - 40774297949567 z^3 + 467660013400125 z^4 + 10902547701971205 z^5 + 25420441954405435 z^6 + 16220916415504515 z^7 + 2931152853724095 z^8 + 103290668856375 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (14169505792 - 328942862976 z + 4117225185801 z^2 - 40774297949567 z^3 + 467660013400125 z^4 + 10902547701971205 z^5 + 25420441954405435 z^6 + 16220916415504515 z^7 + 2931152853724095 z^8 + 103290668856375 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (14169505792 - 328942862976 z + 4117225185801 z^2 - 40774297949567 z^3 + 467660013400125 z^4 + 10902547701971205 z^5 + 25420441954405435 z^6 + 16220916415504515 z^7 + 2931152853724095 z^8 + 103290668856375 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-14169505792 + 337798804096 z - 4321361547321 z^2 + 43314515257832 z^3 - 492737169551900 z^4 + 15267692027813400 z^5 + 77486036787393290 z^6 + 93419958795219160 z^7 + 34690964331231780 z^8 + 3569029958293800 z^9 + 55889533554855 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (6784796489924280272445 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]