Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2300)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=9/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.2300.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(1/2), 2}, z] == (1/135135) (E^(z/2) (135135 + 3275910 z - 29325576 z^2 + 46972032 z^3 - 25121280 z^4 + 4907008 z^5 - 294912 z^6) BesselI[0, z/2]) + (1/135135) (E^(z/2) (4455 + 275394 z + 7636872 z^2 - 28326528 z^3 + 20656640 z^4 - 4612096 z^5 + 294912 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]