Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab09)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=6

http://functions.wolfram.com/07.23.03.ab09.01

Input Form

Hypergeometric2F1[-(17/4), 6, 19/4, z] == (1/(137438953472 z^(15/4))) (55 (2 z^(3/4) (-51051 - 356031 z - 2329119 z^2 + 1223796973 z^3 - 6072597489 z^4 + 10954333299 z^5 - 8567531973 z^6 + 2464997535 z^7) + 13923 (-1 + z)^3 (11 + 105 z + 750 z^2 + 7250 z^3 - 119625 z^4 + 177045 z^5) ArcTan[z^(1/4)] - 13923 (-1 + z)^3 (11 + 105 z + 750 z^2 + 7250 z^3 - 119625 z^4 + 177045 z^5) ArcTanh[z^(1/4)]))

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]