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

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=9/8

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

Input Form

Hypergeometric2F1[-(37/8), 9/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (-457080832 + 4011955584 z - 15473388567 z^2 + 33953400390 z^3 - 43860259170 z^4 + 54561332504 z^5 - 38949928703 z^6 + 17314191114 z^7 - 4431608720 z^8 + 500697120 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-457080832 + 4011955584 z - 15473388567 z^2 + 33953400390 z^3 - 43860259170 z^4 + 54561332504 z^5 - 38949928703 z^6 + 17314191114 z^7 - 4431608720 z^8 + 500697120 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-457080832 + 4297631104 z - 17933992167 z^2 + 43234855755 z^3 - 63673976730 z^4 + 10701073334 z^5 - 7260372763 z^6 + 3094607519 z^7 - 763437620 z^8 + 83449520 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-457080832 + 4011955584 z - 15473388567 z^2 + 33953400390 z^3 - 43860259170 z^4 + 54561332504 z^5 - 38949928703 z^6 + 17314191114 z^7 - 4431608720 z^8 + 500697120 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (17937727563921165 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]