Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4555)

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=3, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=5

http://functions.wolfram.com/07.25.03.4555.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {5, 5}, z] == (1536 (-6 + 17 z))/(12155 z^4) - (1/(139618103625 z^4)) (1024 E^(z/2) (-103378275 + 344594250 z - 109909440 z^2 - 24175350 z^3 - 149905440 z^4 + 126178380 z^5 - 35020800 z^6 + 4266096 z^7 - 232320 z^8 + 4576 z^9) BesselI[0, z/2]) + (1/(139618103625 z^3)) (256 E^(z/2) (688068135 - 662481000 z - 248038560 z^2 - 260663760 z^3 + 387583200 z^4 - 124357824 z^5 + 16162560 z^6 - 910976 z^7 + 18304 z^8) 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]
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