Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8cc)

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=47/8

http://functions.wolfram.com/07.23.03.b8cc.01

Input Form

Hypergeometric2F1[-(43/8), 47/8, 5, z] == (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (579769344 + 3424262688 z + 20618613477 z^2 + 195822757746 z^3 - 7451583546675 z^4 + 35768905267980 z^5 - 73114932975440 z^6 + 75819204215040 z^7 - 39454985306880 z^8 + 8213528294400 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-72471168 - 480687669 z - 2931685218 z^2 - 4062589301925 z^3 + 24572592149100 z^4 - 57504969774960 z^5 + 65775995633920 z^6 - 36990926818560 z^7 + 8213528294400 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-72471168 - 439922637 z - 2653124166 z^2 + 2396630018475 z^3 - 15690792161280 z^4 + 42092756100840 z^5 - 59345592650240 z^6 + 46496312628480 z^7 - 19231676006400 z^8 + 3285411317760 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (579769344 + 3424262688 z + 20618613477 z^2 + 195822757746 z^3 - 7451583546675 z^4 + 35768905267980 z^5 - 73114932975440 z^6 + 75819204215040 z^7 - 39454985306880 z^8 + 8213528294400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (396749539611550125 Pi z^4)

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]