Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aiu9)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-9/2

http://functions.wolfram.com/07.25.03.aiu9.01

Input Form

HypergeometricPFQ[{5/2, 3}, {-(9/2), -(3/2)}, -z] == (1/8505) (8505 - 9450 z + 37800 z^2 + 226800 z^3 + 831600 z^4 + 6054048 z^5 - 13628160 z^6 + 8163840 z^7 - 2042112 z^8 + 239616 z^9 - 12928 z^10 + 256 z^11) - (1/8505) ((64 Sqrt[Pi] (163800 z^(11/2) - 264600 z^(13/2) + 141876 z^(15/2) - 33684 z^(17/2) + 3843 z^(19/2) - 204 z^(21/2) + 4 z^(23/2)) 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]