Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anc1)

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=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.anc1.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), 1/2}, -z] == (1/29469825) (29469825 + 294698250 z + 851350500 z^2 + 1702701000 z^3 + 3308104800 z^4 + 8380532160 z^5 + 53330659200 z^6 - 116038137600 z^7 + 79937383680 z^8 - 26721636480 z^9 + 4989333888 z^10 - 551830560 z^11 + 36684960 z^12 - 1428672 z^13 + 29824 z^14 - 256 z^15) + (1/29469825) ((16 Sqrt[Pi] (-5640742800 z^(13/2) + 9186352560 z^(15/2) - 5709474540 z^(17/2) + 1811266380 z^(19/2) - 328035015 z^(21/2) + 35593425 z^(23/2) - 2336544 z^(25/2) + 90216 z^(27/2) - 1872 z^(29/2) + 16 z^(31/2)) 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]