Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa25)

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=4, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=4, b₁=5

http://functions.wolfram.com/07.25.03.aa25.01

Input Form

HypergeometricPFQ[{-(3/2), 4}, {5, 5}, z] == 1024/(385 z^4) + (1/(4002075 z^4)) (128 E^(z/2) (-83160 + 41580 z + 14793 z^2 + 8196 z^3 + 36420 z^4 - 18200 z^5 + 1680 z^6) BesselI[0, z/2]) - (1/(4002075 z^3)) (128 E^(z/2) (79962 + 36249 z + 22356 z^2 + 20740 z^3 - 16520 z^4 + 1680 z^5) 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]