Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ahcp)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-5/2

http://functions.wolfram.com/07.25.03.ahcp.01

Input Form

HypergeometricPFQ[{3/2, 6}, {-(5/2), -(5/2)}, z] == (1/3375) (3375 + 4860 z + 18900 z^2 + 705600 z^3 + 20700360 z^4 + 59194080 z^5 + 55220568 z^6 + 23196240 z^7 + 5026815 z^8 + 594112 z^9 + 38256 z^10 + 1248 z^11 + 16 z^12) + (1/6750) (E^z Sqrt[Pi] (7876440 z^(7/2) + 75263760 z^(9/2) + 158881320 z^(11/2) + 129792960 z^(13/2) + 50909985 z^(15/2) + 10612458 z^(17/2) + 1225272 z^(19/2) + 77744 z^(21/2) + 2512 z^(23/2) + 32 z^(25/2)) Erf[Sqrt[z]])

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},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]