Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2173)

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=6

http://functions.wolfram.com/07.25.03.2173.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {6, 6}, z] == (5120 (-8 + 21 z))/(29393 z^5) + (1/(80826697146195 z^5)) (256 E^(z/2) (439977938400 - 1374931057500 z + 424665835965 z^2 + 85088036250 z^3 + 38379693240 z^4 + 342086663520 z^5 - 317235819600 z^6 + 100728067104 z^7 - 14971911360 z^8 + 1122760704 z^9 - 40784640 z^10 + 565760 z^11) BesselI[0, z/2]) - (1/(80826697146195 z^4)) (256 E^(z/2) (-721215317340 + 610755252975 z + 183113596890 z^2 + 114733551240 z^3 + 138834914400 z^4 - 235903240944 z^5 + 87322398240 z^6 - 13908630336 z^7 + 1082824704 z^8 - 40218880 z^9 + 565760 z^10) 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]