Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7vq)

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=-23/4, b>=a

For fixed z and a=-23/4, b=6

http://functions.wolfram.com/07.23.03.a7vq.01

Input Form

Hypergeometric2F1[-(23/4), 6, 9/4, z] == (1/(4294967296 z^(5/4))) (-2 z^(1/4) (5552085 - 1407945926 z + 16092556947 z^2 - 62572346676 z^3 + 108641317995 z^4 - 87000595110 z^5 + 26239658445 z^6) + 504735 (-1 + z)^2 (11 + 1485 z - 30690 z^2 + 153450 z^3 - 272025 z^4 + 155961 z^5) ArcTan[z^(1/4)] + 504735 (-1 + z)^2 (11 + 1485 z - 30690 z^2 + 153450 z^3 - 272025 z^4 + 155961 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]