Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al90)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.al90.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(11/2), 1}, z] == (1/16372125) (E^(z/2) (16372125 - 55069875 z + 83481300 z^2 - 97505100 z^3 + 116424000 z^4 - 185623200 z^5 + 741484800 z^6 + 2460084480 z^7 + 1820125440 z^8 + 568992000 z^9 + 88181760 z^10 + 7040000 z^11 + 274432 z^12 + 4096 z^13) BesselI[0, z/2]) + (1/16372125) (E^(z/2) (21796425 z - 42600600 z^2 + 51993900 z^3 - 58716000 z^4 + 77666400 z^5 - 161118720 z^6 + 1277418240 z^7 + 1364336640 z^8 + 490579200 z^9 + 81541120 z^10 + 6771712 z^11 + 270336 z^12 + 4096 z^13) 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]