Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4547)

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=3, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=4

http://functions.wolfram.com/07.25.03.4547.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {4, 5}, z] == 384/(715 z^3) - (1/(8212829625 z^3)) (32 E^(z/2) (137837700 - 62837775 z - 21021480 z^2 - 273272760 z^3 + 276951600 z^4 - 91992240 z^5 + 13128000 z^6 - 821568 z^7 + 18304 z^8) BesselI[0, z/2]) + (1/(8212829625 z^3)) (32 E^(z/2) (24324300 - 118545345 z - 71470440 z^2 - 100901160 z^3 + 202330800 z^4 - 80041680 z^5 + 12333888 z^6 - 803264 z^7 + 18304 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]