Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa82)

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=-3/2, a₂>=-3/2

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

For fixed z and a₁=-3/2, a₂=5, b₁=-9/2

http://functions.wolfram.com/07.25.03.aa82.01

Input Form

HypergeometricPFQ[{-(3/2), 5}, {-(9/2), -(9/2)}, -z] == (1/893025) (893025 + 330750 z + 40500 z^2 - 7560 z^3 + 10080 z^4 - 181440 z^5 + 2721960 z^6 - 4041960 z^7 + 1946988 z^8 - 406884 z^9 + 40504 z^10 - 1872 z^11 + 32 z^12) - (1/893025) ((2 Sqrt[Pi] (-377910 z^(11/2) + 2063970 z^(13/2) - 2427345 z^(15/2) + 1066185 z^(17/2) - 213120 z^(19/2) + 20712 z^(21/2) - 944 z^(23/2) + 16 z^(25/2)) 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]