Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4952)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=6

http://functions.wolfram.com/07.23.03.4952.01

Input Form

Hypergeometric2F1[-(17/3), 6, 1/3, -z] == (1/15943230) (3 (5314410 + 404991340 z + 3933055315 z^2 + 12728035320 z^3 + 16389889516 z^4 + 7264216960 z^5) + 52360 z^(2/3) (2618 + 52360 z + 301070 z^2 + 711620 z^3 + 737035 z^4 + 277472 z^5) Log[1 + z^(1/3)] + 52360 (-1)^(2/3) z^(2/3) (2618 + 52360 z + 301070 z^2 + 711620 z^3 + 737035 z^4 + 277472 z^5) Log[1 - (-1)^(1/3) z^(1/3)] - 52360 (-1)^(1/3) z^(2/3) (2618 + 52360 z + 301070 z^2 + 711620 z^3 + 737035 z^4 + 277472 z^5) Log[1 + (-1)^(2/3) z^(1/3)])

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]