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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(9/2), 1/2}, -z] == (1/297675) (297675 + 2976750 z + 9355500 z^2 + 22702680 z^3 + 64864800 z^4 + 441080640 z^5 - 1015822080 z^6 + 703261440 z^7 - 226606464 z^8 + 39060960 z^9 - 3785208 z^10 + 204816 z^11 - 5728 z^12 + 64 z^13) - (1/297675) ((4 Sqrt[Pi] (190466640 z^(11/2) - 322328160 z^(13/2) + 200234160 z^(15/2) - 61118820 z^(17/2) + 10214505 z^(19/2) - 971208 z^(21/2) + 51912 z^(23/2) - 1440 z^(25/2) + 16 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]