Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3169)

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=-5/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=-5/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.3169.01

Input Form

HypergeometricPFQ[{-(9/2), -(5/2)}, {-(7/2), 4}, z] == (1/(4729725 z)) (4 E^(z/2) (12285 + 1215270 z - 1455300 z^2 + 487200 z^3 - 49200 z^4 - 96 z^5 + 128 z^6) BesselI[0, z/2]) - (1/(4729725 z^2)) (4 E^(z/2) (49140 + 131355 z + 345870 z^2 - 1041180 z^3 + 438240 z^4 - 49104 z^5 + 32 z^6 + 128 z^7) 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]