Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bco2)

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=-1/8

http://functions.wolfram.com/07.23.03.bco2.01

Input Form

Hypergeometric2F1[-(35/8), -(1/8), 6, z] == (1/(29834332625876625 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-13074432 + 156433536 z - 897119181 z^2 + 3433659537 z^3 - 11615269050 z^4 - 143561975430 z^5 - 1967564785 z^6 + 423500685 z^7 - 67999320 z^8 + 5436600 z^9) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (408576 - 4591692 z + 24727626 z^2 - 89645325 z^3 - 9184640850 z^4 - 463595610 z^5 + 101071970 z^6 - 16592085 z^7 + 1359150 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1634304 - 19286064 z + 109057473 z^2 - 412236825 z^3 + 24151043070 z^4 + 7781886510 z^5 - 961689235 z^6 + 197693595 z^7 - 29483100 z^8 + 2174640 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-13074432 + 156433536 z - 897119181 z^2 + 3433659537 z^3 - 11615269050 z^4 - 143561975430 z^5 - 1967564785 z^6 + 423500685 z^7 - 67999320 z^8 + 5436600 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]