Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4kl)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=6, b>=a

For fixed z and a=6, b=6

http://functions.wolfram.com/07.23.03.b4kl.01

Input Form

Hypergeometric2F1[6, 6, 8/5, z] == (9 (26365189 + 291011540 z + 566482050 z^2 + 245871500 z^3 + 17550625 z^4))/ (244140625 (-1 + z)^10) + (3927 Sqrt[10 - 2 Sqrt[5]] (2618 + 163625 z + 935000 z^2 + 1168750 z^3 + 343750 z^4 + 15625 z^5) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (1220703125 (1 - z)^(52/5) z^(3/5)) - (3927 Sqrt[2 (5 + Sqrt[5])] (2618 + 163625 z + 935000 z^2 + 1168750 z^3 + 343750 z^4 + 15625 z^5) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/ (4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (1220703125 (1 - z)^(52/5) z^(3/5)) + (7854 (2618 + 163625 z + 935000 z^2 + 1168750 z^3 + 343750 z^4 + 15625 z^5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1220703125 (1 - z)^(52/5) z^(3/5)) - (3927 (1 + Sqrt[5]) (2618 + 163625 z + 935000 z^2 + 1168750 z^3 + 343750 z^4 + 15625 z^5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/ (2441406250 (1 - z)^(52/5) z^(3/5)) + (3927 (-1 + Sqrt[5]) (2618 + 163625 z + 935000 z^2 + 1168750 z^3 + 343750 z^4 + 15625 z^5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/ (2441406250 (1 - z)^(52/5) z^(3/5))

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]