Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anor)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.anor.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 2}, z] == (1/13395375) (E^(z/2) (13395375 - 87450300 z + 416499300 z^2 - 3735448920 z^3 - 24094193760 z^4 - 37092867840 z^5 - 24725917440 z^6 - 8479296000 z^7 - 1612160256 z^8 - 174425088 z^9 - 10560512 z^10 - 329728 z^11 - 4096 z^12) BesselI[0, z/2]) + (1/13395375) (E^(z/2) (-1157625 + 21224700 z - 105609420 z^2 + 525009240 z^3 - 7695727200 z^4 - 21374357760 z^5 - 18216334080 z^6 - 7099577856 z^7 - 1452619008 z^8 - 164346880 z^9 - 10236928 z^10 - 325632 z^11 - 4096 z^12) 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]