Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0413)

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=-7/2

http://functions.wolfram.com/07.25.03.0413.01

Input Form

HypergeometricPFQ[{-(11/2), -(5/2)}, {-(7/2), 3}, z] == -((1/14189175) (8 E^(z/2) (-1787940 + 3128895 z - 1577520 z^2 + 248880 z^3 + 1920 z^4 - 2736 z^5 + 128 z^6) BesselI[0, z/2])) + (1/(14189175 z)) (4 E^(z/2) (-114345 - 644490 z + 3824730 z^2 - 2665920 z^3 + 494160 z^4 - 1248 z^5 - 5216 z^6 + 256 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]