Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2122)

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=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=2

http://functions.wolfram.com/07.25.03.2122.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {2, 3}, z] == (1/405405) (E^(z/2) (405405 - 1683990 z + 2002986 z^2 - 948000 z^3 + 196656 z^4 - 17568 z^5 + 544 z^6) BesselI[0, z/2]) - (1/405405) (2 E^(z/2) (10395 - 318348 z + 650775 z^2 - 388032 z^3 + 89952 z^4 - 8512 z^5 + 272 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]