Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5284)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=5, b₁=1

http://functions.wolfram.com/07.25.03.5284.01

Input Form

HypergeometricPFQ[{-(9/2), 5}, {1, 6}, z] == (1/(43648605 z^3)) (E^(z/2) (725760 - 362880 z + 113400 z^2 + 43622145 z^3 - 185501610 z^4 + 188918004 z^5 - 67528032 z^6 + 9094800 z^7 - 388960 z^8) BesselI[0, z/2]) + (1/(43648605 z^4)) (E^(z/2) (-2903040 + 1451520 z - 544320 z^2 + 151200 z^3 - 33075 z^4 + 73654314 z^5 - 133865292 z^6 + 59016672 z^7 - 8705840 z^8 + 388960 z^9) 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]