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

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=9/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(5/2), 1}, z] == (1/165375) (E^(z/2) (165375 - 1422225 z + 7358400 z^2 - 66413340 z^3 - 416067120 z^4 - 605886960 z^5 - 370251840 z^6 - 112062720 z^7 - 17903872 z^8 - 1515776 z^9 - 63488 z^10 - 1024 z^11) BesselI[0, z/2]) + (1/165375) (E^(z/2) (300825 z - 1813140 z^2 + 9378180 z^3 - 136308480 z^4 - 360361680 z^5 - 280969920 z^6 - 96250112 z^7 - 16480256 z^8 - 1453824 z^9 - 62464 z^10 - 1024 z^11) BesselI[1, z/2])

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]