Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7jf)

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=-17/8

http://functions.wolfram.com/07.23.03.b7jf.01

Input Form

Hypergeometric2F1[-(43/8), -(17/8), 5, z] == (1/(20474541998150625 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-7529472 + 143765856 z - 1539843201 z^2 + 15612139602 z^3 + 922497913625 z^4 + 1786201930520 z^5 + 611652349665 z^6 + 1430474010 z^7 - 97848345 z^8 + 4391100 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (941184 - 17286903 z + 179986734 z^2 + 206455879575 z^3 + 453536636000 z^4 + 172508340935 z^5 + 1402078230 z^6 - 96531015 z^7 + 4391100 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (941184 - 17816319 z + 189604458 z^2 - 126887963625 z^3 - 332748036580 z^4 - 188623409065 z^5 - 19666712310 z^6 + 613070745 z^7 - 40983600 z^8 + 1756440 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-7529472 + 143765856 z - 1539843201 z^2 + 15612139602 z^3 + 922497913625 z^4 + 1786201930520 z^5 + 611652349665 z^6 + 1430474010 z^7 - 97848345 z^8 + 4391100 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

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]