Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alt4)

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=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=1

http://functions.wolfram.com/07.25.03.alt4.01

Input Form

HypergeometricPFQ[{7/2, 6}, {1, 1}, z] == (1/14400) (E^(z/2) (14400 + 295200 z + 1030770 z^2 + 1262985 z^3 + 684150 z^4 + 179620 z^5 + 23360 z^6 + 1424 z^7 + 32 z^8) BesselI[0, z/2]) + (1/14400) (E^(z/2) (38520 z + 404460 z^2 + 788535 z^3 + 535550 z^4 + 158300 z^5 + 21984 z^6 + 1392 z^7 + 32 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]