Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anw2)

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=1

http://functions.wolfram.com/07.25.03.anw2.01

Input Form

HypergeometricPFQ[{11/2, 6}, {1, 2}, z] == (1/453600) (E^(z/2) (453600 + 7257600 z + 24389055 z^2 + 31186305 z^3 + 18726120 z^4 + 5804280 z^5 + 966000 z^6 + 85776 z^7 + 3776 z^8 + 64 z^9) BesselI[0, z/2]) + (1/453600) (E^(z/2) (1101780 z + 9577080 z^2 + 18849735 z^3 + 14141520 z^4 + 4956120 z^5 + 885696 z^6 + 82096 z^7 + 3712 z^8 + 64 z^9) 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]