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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=6, b₁=1/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {1/2, 1/2}, -z] == (1/56700) (56700 - 6237000 z + 43659000 z^2 - 82577880 z^3 + 64045080 z^4 - 24507285 z^5 + 5065095 z^6 - 586080 z^7 + 37552 z^8 - 1232 z^9 + 16 z^10) + (1/113400) ((Sqrt[Pi] (-1247400 Sqrt[z] + 31185000 z^(3/2) - 138461400 z^(5/2) + 213305400 z^(7/2) - 148700475 z^(9/2) + 53576775 z^(11/2) - 10681650 z^(13/2) + 1208520 z^(15/2) - 76320 z^(17/2) + 2480 z^(19/2) - 32 z^(21/2)) 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]