Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bck9)

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=-35/8, b>=a

For fixed z and a=-35/8, b=-15/8

http://functions.wolfram.com/07.23.03.bck9.01

Input Form

Hypergeometric2F1[-(35/8), -(15/8), 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-40449024 + 650133792 z - 5753755161 z^2 + 47277838377 z^3 + 760945973206 z^4 + 754996165938 z^5 + 88017747363 z^6 - 3534371659 z^7 + 146376048 z^8) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 4 (-10112256 + 166325544 z - 1498351932 z^2 + 12342758967 z^3 - 193435633421 z^4 - 476508200442 z^5 - 162196150830 z^6 - 222613573 z^7 + 9148503 z^8) 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) (-40449024 + 650133792 z - 5753755161 z^2 + 47277838377 z^3 + 760945973206 z^4 + 754996165938 z^5 + 88017747363 z^6 - 3534371659 z^7 + 146376048 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-40449024 + 650133792 z - 5753755161 z^2 + 47277838377 z^3 + 760945973206 z^4 + 754996165938 z^5 + 88017747363 z^6 - 3534371659 z^7 + 146376048 z^8) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (49725942297980949 Pi (1 + Sqrt[1 - z])^(1/4) 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]