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

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.anot.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 3}, z] == -((1/13395375) (16 E^(z/2) (-850500 + 3765825 z - 13343400 z^2 + 94324230 z^3 + 495371520 z^4 + 613811520 z^5 + 323688960 z^6 + 85691520 z^7 + 12125184 z^8 + 919296 z^9 + 34816 z^10 + 512 z^11) BesselI[0, z/2])) - (1/(13395375 z)) (4 E^(z/2) (212625 + 472500 z - 4573800 z^2 + 15853320 z^3 - 60936120 z^4 + 737936640 z^5 + 1554577920 z^6 + 1014750720 z^7 + 299379456 z^8 + 45026304 z^9 + 3540992 z^10 + 137216 z^11 + 2048 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]