Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an3r)

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=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.an3r.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(3/2), -(3/2)}, -z] == (1/14175) (14175 - 170100 z + 13097700 z^2 - 713512800 z^3 + 3567564000 z^4 - 5641075440 z^5 + 4003159680 z^6 - 1496130660 z^7 + 319951080 z^8 - 40749450 z^9 + 3114024 z^10 - 138768 z^11 + 3296 z^12 - 32 z^13) + (1/14175) ((Sqrt[Pi] (-97297200 z^(5/2) + 1556755200 z^(7/2) - 5378373000 z^(9/2) + 7159698000 z^(11/2) - 4630452750 z^(13/2) + 1639050840 z^(15/2) - 338927715 z^(17/2) + 42241050 z^(19/2) - 3181800 z^(21/2) + 140400 z^(23/2) - 3312 z^(25/2) + 32 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]