Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.anj2)

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=5, b>=a

For fixed z and a=5, b=21/4

http://functions.wolfram.com/07.23.03.anj2.01

Input Form

Hypergeometric2F1[5, 21/4, -(21/4), z] == (1/(2652 (-1 + z)^16)) (-4 (-663 + 13923 z - 147225 z^2 + 1079205 z^3 - 6594310 z^4 + 42622174 z^5 - 783120114 z^6 - 1697720961 z^7 + 681329259 z^8 + 1425641019 z^9 + 324767773 z^10 + 12129920 z^11) + 4389 Sqrt[1 - z] z^(25/4) (483923 + 1134716 z + 670514 z^2 + 108732 z^3 + 3315 z^4) Beta[z, 3/4, 1/2])

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]