Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5447)

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/07.25.03.5447.01

Input Form

HypergeometricPFQ[{-(9/2), 11/2}, {-(3/2), 3}, z] == -((1/135135) (4 E^(z/2) (-33915 - 168000 z - 953856 z^2 + 3205120 z^3 - 1900544 z^4 + 262144 z^5) BesselI[0, z/2])) + (1/(135135 z)) (4 E^(z/2) (-525 + 3675 z + 48576 z^2 + 186880 z^3 + 1697792 z^4 - 1638400 z^5 + 262144 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]