Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2340)

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=3/2

http://functions.wolfram.com/07.25.03.2340.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {3/2, 3}, z] == (1/3378375) (8 E^(z/2) (422235 - 2531430 z + 3870300 z^2 - 2248980 z^3 + 556080 z^4 - 57856 z^5 + 2048 z^6) BesselI[0, z/2]) - (1/(3378375 z)) (4 E^(z/2) (-495 + 18810 z - 1533360 z^2 + 4596000 z^3 - 3547080 z^4 + 1002592 z^5 - 111616 z^6 + 4096 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]