Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.all3)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.all3.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(9/2), 5}, z] == -((1/(4465125 z^2)) (32 E^(z/2) (103378275 - 54729675 z + 17406900 z^2 - 4025700 z^3 + 680400 z^4 - 35280 z^5 - 80640 z^6 + 264960 z^7 + 602880 z^8 + 226560 z^9 + 27648 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(4465125 z^3)) (32 E^(z/2) (-413513100 + 218918700 z - 83108025 z^2 + 23700600 z^3 - 5386500 z^4 + 1048320 z^5 - 206640 z^6 + 69120 z^7 - 72960 z^8 + 414720 z^9 + 200448 z^10 + 26624 z^11 + 1024 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]