Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5rz)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5rz.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (102945792 + 584431840 z + 3409576695 z^2 + 31703081550 z^3 - 877702012453 z^4 + 3820024118064 z^5 - 7277289465600 z^6 + 7126248898560 z^7 - 3531161272320 z^8 + 704136609792 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (102945792 + 584431840 z + 3409576695 z^2 + 31703081550 z^3 - 877702012453 z^4 + 3820024118064 z^5 - 7277289465600 z^6 + 7126248898560 z^7 - 3531161272320 z^8 + 704136609792 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (102945792 + 584431840 z + 3409576695 z^2 + 31703081550 z^3 - 877702012453 z^4 + 3820024118064 z^5 - 7277289465600 z^6 + 7126248898560 z^7 - 3531161272320 z^8 + 704136609792 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (51472896 + 272913584 z + 1589929395 z^2 + 15179477670 z^3 + 525381857371 z^4 - 4416496550004 z^5 + 13422935056608 z^6 - 20706900234240 z^7 + 17486776074240 z^8 - 7737120129024 z^9 + 1408273219584 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(63594152067451005 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]