Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa2n)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.aa2n.01

Input Form

HypergeometricPFQ[{-(3/2), 9/2}, {-(11/2), 3}, z] == (1/363825) (4 E^(z/2) (105435 - 32400 z - 8040 z^2 + 6720 z^3 - 1680 z^4 + 128 z^5 + 64 z^6) BesselI[0, z/2]) + (1/(363825 z)) (4 E^(z/2) (-57915 + 96525 z - 9960 z^2 - 17160 z^3 + 8400 z^4 - 1712 z^5 + 64 z^6 + 64 z^7) 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]