Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akm6)

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, a₂>=3

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

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

http://functions.wolfram.com/07.25.03.akm6.01

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(3/2)}, -z] == (1/29469825) (29469825 - 58939650 z + 340540200 z^2 + 2432430000 z^3 + 8270262000 z^4 + 29331862560 z^5 + 234654900480 z^6 - 673428349440 z^7 + 569506049280 z^8 - 225104140800 z^9 + 48455497728 z^10 - 6064521216 z^11 + 449691648 z^12 - 19310592 z^13 + 440320 z^14 - 4096 z^15) + (1/29469825) ((1024 Sqrt[Pi] (-424116000 z^(13/2) + 865196640 z^(15/2) - 648149040 z^(17/2) + 240997680 z^(19/2) - 50083110 z^(21/2) + 6133050 z^(23/2) - 448371 z^(25/2) + 19071 z^(27/2) - 432 z^(29/2) + 4 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]