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

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=-5/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(5/2), -(5/2)}, -z] == (1/212625) (212625 - 561330 z + 3243240 z^2 - 162162000 z^3 + 6226521840 z^4 - 22999062240 z^5 + 27582605568 z^6 - 14991450624 z^7 + 4279246080 z^8 - 688507392 z^9 + 63977472 z^10 - 3371008 z^11 + 92672 z^12 - 1024 z^13) + (1/212625) ((256 Sqrt[Pi] (3991680 z^(7/2) - 47900160 z^(9/2) + 127008000 z^(11/2) - 131120640 z^(13/2) + 65832480 z^(15/2) - 17950464 z^(17/2) + 2808288 z^(19/2) - 256320 z^(21/2) + 13347 z^(23/2) - 364 z^(25/2) + 4 z^(27/2)) 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]