Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aiq0)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.aiq0.01

Input Form

HypergeometricPFQ[{5/2, 5/2}, {-(9/2), 2}, z] == (1/8505) (E^(z/2) (8505 - 7560 z + 4824 z^2 - 3312 z^3 + 3120 z^4 - 7488 z^5 - 14784 z^6 - 3968 z^7 - 256 z^8) BesselI[0, z/2]) + (1/8505) (E^(z/2) (-10395 + 8424 z - 4392 z^2 + 2352 z^3 - 1680 z^4 + 2112 z^5 - 11200 z^6 - 3712 z^7 - 256 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]
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]