Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1412)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=5

http://functions.wolfram.com/07.25.03.1412.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {5, 5}, z] == (192 (48 - 304 z + 323 z^2))/(20995 z^4) + (1/(4582012309875 z^4)) (512 E^(z/2) (-3928374450 + 26843892075 z - 37188687870 z^2 + 8599297320 z^3 + 10624939200 z^4 - 7148487600 z^5 + 1810640160 z^6 - 230125632 z^7 + 15401472 z^8 - 513280 z^9 + 6656 z^10) BesselI[0, z/2]) - (1/(4582012309875 z^3)) (512 E^(z/2) (7725497445 - 24528427470 z + 12480419160 z^2 + 5610252960 z^3 - 5640693840 z^4 + 1602129312 z^5 - 215474112 z^6 + 14898176 z^7 - 506624 z^8 + 6656 z^9) 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]