Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b770)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b770.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (64276992 + 185465904 z + 745922775 z^2 + 5395752180 z^3 - 118100228141 z^4 + 441387564002 z^5 - 743152265856 z^6 + 655268190720 z^7 - 296331509760 z^8 + 54486761472 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 2 Sqrt[1 - z] (64276992 + 185465904 z + 745922775 z^2 + 5395752180 z^3 - 118100228141 z^4 + 441387564002 z^5 - 743152265856 z^6 + 655268190720 z^7 - 296331509760 z^8 + 54486761472 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (64276992 + 185465904 z + 745922775 z^2 + 5395752180 z^3 - 118100228141 z^4 + 441387564002 z^5 - 743152265856 z^6 + 655268190720 z^7 - 296331509760 z^8 + 54486761472 z^9) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (128553984 + 322724064 z + 1339564317 z^2 + 10187024445 z^3 + 306990970223 z^4 - 2211709586009 z^5 + 5932525105584 z^6 - 8227891845888 z^7 + 6331731394560 z^8 - 2579517997056 z^9 + 435894091776 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (17937727563921165 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^4)

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

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]