Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7fc)

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=-33/8

http://functions.wolfram.com/07.23.03.b7fc.01

Input Form

Hypergeometric2F1[-(43/8), -(33/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (139493376 - 3294986112 z + 41761659555 z^2 - 414940449528 z^3 + 4688624603124 z^4 + 374394678731768 z^5 + 1206524420461874 z^6 + 1052778017998520 z^7 + 277646643544116 z^8 + 17120966161992 z^9 + 3819891075 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-17436672 + 399204432 z - 4931389683 z^2 + 48312135333 z^3 + 81475781396625 z^4 + 293087612173529 z^5 + 275747554032071 z^6 + 77696307726191 z^7 + 5140371544539 z^8 + 3819891075 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-8718336 + 204506280 z - 2576987721 z^2 + 25520987448 z^3 - 24897103238700 z^4 - 100923017106248 z^5 - 115450424603750 z^6 - 45862427908088 z^7 - 5997883499916 z^8 - 171131120160 z^9 + 763978215 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (139493376 - 3294986112 z + 41761659555 z^2 - 414940449528 z^3 + 4688624603124 z^4 + 374394678731768 z^5 + 1206524420461874 z^6 + 1052778017998520 z^7 + 277646643544116 z^8 + 17120966161992 z^9 + 3819891075 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (64508729982733211175 Pi 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]