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

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=11/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=11/2, b₁=-3/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(3/2), 3}, z] == (1/297675) (8 E^(z/2) (37800 - 222075 z + 1920240 z^2 + 11032560 z^3 + 14253120 z^4 + 7413840 z^5 + 1814400 z^6 + 218112 z^7 + 12288 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(297675 z)) (4 E^(z/2) (-4725 - 9450 z + 107730 z^2 - 564480 z^3 + 7746480 z^4 + 17992800 z^5 + 11783520 z^6 + 3227904 z^7 + 412416 z^8 + 24064 z^9 + 512 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]