Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0381)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=-5/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.0381.01

Input Form

HypergeometricPFQ[{-(11/2), -(5/2)}, {-(9/2), 1}, z] == (1/654885) (E^(z/2) (654885 - 2328480 z + 1740312 z^2 - 320376 z^3 - 120 z^4 - 192 z^5 + 256 z^6) BesselI[0, z/2]) - (4 E^(z/2) (-265923 z + 355299 z^2 - 80004 z^3 + 18 z^4 + 16 z^5 + 64 z^6) BesselI[1, z/2])/654885

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]