Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4170)

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=-9/2, a₂>=-9/2

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

For fixed z and a₁=-9/2, a₂=2, b₁=4

http://functions.wolfram.com/07.25.03.4170.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {4, 6}, z] == (96 (-4 + 5 z))/(143 z^3) - (1/(31208752575 z^3)) (128 E^(z/2) (-658783125 + 1118917800 z - 269066520 z^2 - 295349040 z^3 + 176446800 z^4 - 37212480 z^5 + 3648960 z^6 - 166272 z^7 + 2816 z^8) BesselI[0, z/2]) + (1/(31208752575 z^4)) (128 E^(z/2) (-16216200 - 107432325 z + 723732120 z^2 - 386802360 z^3 - 165007440 z^4 + 144231120 z^5 - 33804480 z^6 + 3486912 z^7 - 163456 z^8 + 2816 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]
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