Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2214)

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=-9/2

http://functions.wolfram.com/07.25.03.2214.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(9/2), 4}, z] == -((1/(402026625 z)) (4 E^(z/2) (7432425 - 110540430 z - 74511360 z^2 - 19353600 z^3 - 6881280 z^4 - 3932160 z^5 - 6291456 z^6 + 8388608 z^7) BesselI[0, z/2])) + (1/(402026625 z^2)) (4 E^(z/2) (29729700 - 40135095 z + 54656910 z^2 + 60963840 z^3 + 15052800 z^4 + 4915200 z^5 + 2359296 z^6 + 2097152 z^7 + 8388608 z^8) 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]