Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc9a)

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=-37/8, b>=a

For fixed z and a=-37/8, b=41/8

http://functions.wolfram.com/07.23.03.bc9a.01

Input Form

Hypergeometric2F1[-(37/8), 41/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (-457080832 - 387447424 z - 487922071 z^2 - 938935088 z^3 - 3716780795 z^4 + 152501090002 z^5 - 466450045296 z^6 + 577192103136 z^7 - 329258426112 z^8 + 72100385280 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-457080832 - 387447424 z - 487922071 z^2 - 938935088 z^3 - 3716780795 z^4 + 152501090002 z^5 - 466450045296 z^6 + 577192103136 z^7 - 329258426112 z^8 + 72100385280 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-457080832 - 101771904 z - 198898791 z^2 - 572285623 z^3 - 3047926245 z^4 + 39594048027 z^5 - 100127261416 z^6 + 110959495056 z^7 - 58452812352 z^8 + 12016730880 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-457080832 - 387447424 z - 487922071 z^2 - 938935088 z^3 - 3716780795 z^4 + 152501090002 z^5 - 466450045296 z^6 + 577192103136 z^7 - 329258426112 z^8 + 72100385280 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (30243634031335725 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

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]