Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4285)

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=5/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=5/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.4285.01

Input Form

HypergeometricPFQ[{-(9/2), 5/2}, {-(3/2), 3}, z] == -((1/135135) (8 E^(z/2) (-18270 - 31815 z - 105744 z^2 + 262272 z^3 - 107520 z^4 + 10240 z^5) BesselI[0, z/2])) + (1/(135135 z)) (4 E^(z/2) (-11025 + 15750 z + 27858 z^2 + 51936 z^3 + 340224 z^4 - 194560 z^5 + 20480 z^6) 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]