Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.agv5)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.agv5.01

Input Form

HypergeometricPFQ[{3/2, 9/2}, {-(9/2), 1}, z] == (1/99225) (E^(z/2) (99225 - 198450 z + 204750 z^2 - 201600 z^3 + 262800 z^4 - 859680 z^5 - 2317920 z^6 - 1220352 z^7 - 238336 z^8 - 18944 z^9 - 512 z^10) BesselI[0, z/2]) - (1/99225) (2 E^(z/2) (-44100 z + 55125 z^2 - 54000 z^3 + 59760 z^4 - 103680 z^5 + 701136 z^6 + 504448 z^7 + 110080 z^8 + 9216 z^9 + 256 z^10) 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]