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

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=2, a₂>=2

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

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

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

Input Form

HypergeometricPFQ[{2, 11/2}, {-(11/2), -(7/2)}, -z] == (1/1031443875) (1031443875 - 589396500 z + 510810300 z^2 - 972972000 z^3 + 8270262000 z^4 + 125707982400 z^5 + 2053230379200 z^6 - 11778298076160 z^7 + 16623870278400 z^8 - 10175218099200 z^9 + 3273662684160 z^10 - 606044528640 z^11 + 67312054272 z^12 - 4519280640 z^13 + 178176000 z^14 - 3768320 z^15 + 32768 z^16) - (1/1031443875) ((16384 Sqrt[Pi] (299376000 z^(13/2) - 1057795200 z^(15/2) + 1257379200 z^(17/2) - 706527360 z^(19/2) + 216548640 z^(21/2) - 38918880 z^(23/2) + 4241160 z^(25/2) - 281160 z^(27/2) + 10989 z^(29/2) - 231 z^(31/2) + 2 z^(33/2)) Erfi[Sqrt[z]])/E^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]