Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4948)

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=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=5

http://functions.wolfram.com/07.25.03.4948.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {5, 6}, z] == 3072/(2431 z^4) - (1/(530548793775 z^4)) (512 E^(z/2) (1309458150 - 585810225 z - 169974360 z^2 - 98796420 z^3 - 1114902000 z^4 + 1032034920 z^5 - 308608320 z^6 + 39693984 z^7 - 2251392 z^8 + 45760 z^9) BesselI[0, z/2]) + (1/(530548793775 z^4)) (256 E^(z/2) (551350800 - 2014523955 z - 882263160 z^2 - 668474640 z^3 - 886383600 z^4 + 1553147520 z^5 - 544308288 z^6 + 75022464 z^7 - 4411264 z^8 + 91520 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]