Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a94q)

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=1, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=1, b₁=4

http://functions.wolfram.com/07.25.03.a94q.01

Input Form

HypergeometricPFQ[{-(3/2), 1}, {4, 4}, z] == (2 (16 - 72 z + 63 z^2))/(35 z^3) + (32 E^(z/2) (-945 + 4725 z - 5484 z^2 + 2220 z^3 - 336 z^4 + 16 z^5) BesselI[0, z/2])/(33075 z^3) - (32 E^(z/2) (1689 - 3720 z + 1908 z^2 - 320 z^3 + 16 z^4) BesselI[1, z/2])/ (33075 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]