Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7n4)

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.b7n4.01

Input Form

Hypergeometric2F1[-(43/8), -(7/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (18552619008 - 276622448256 z + 2064614685903 z^2 - 10997935703370 z^3 + 58332634782345 z^4 + 517802800347012 z^5 + 190720979741201 z^6 - 21500744661578 z^7 + 3453605625015 z^8 - 427662020240 z^9 + 27323528960 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (18552619008 - 283579680384 z + 2166445735839 z^2 - 11744812237158 z^3 + 62259564285765 z^4 - 683863921145148 z^5 - 842240882698951 z^6 - 5527934145734 z^7 + 882839688003 z^8 - 108196295480 z^9 + 6830882240 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) (18552619008 - 276622448256 z + 2064614685903 z^2 - 10997935703370 z^3 + 58332634782345 z^4 + 517802800347012 z^5 + 190720979741201 z^6 - 21500744661578 z^7 + 3453605625015 z^8 - 427662020240 z^9 + 27323528960 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (18552619008 - 276622448256 z + 2064614685903 z^2 - 10997935703370 z^3 + 58332634782345 z^4 + 517802800347012 z^5 + 190720979741201 z^6 - 21500744661578 z^7 + 3453605625015 z^8 - 427662020240 z^9 + 27323528960 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]