Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0689)

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=-1/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=-1/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.0689.01

Input Form

HypergeometricPFQ[{-(11/2), -(1/2)}, {-(3/2), 4}, z] == -((1/(34459425 z)) (4 E^(z/2) (-93555 - 8877330 z + 7567560 z^2 + 986400 z^3 - 1818480 z^4 + 430368 z^5 - 36672 z^6 + 1024 z^7) BesselI[0, z/2])) + (1/(34459425 z^2)) (4 E^(z/2) (-374220 - 1049895 z - 2765070 z^2 + 6856200 z^3 - 288480 z^4 - 1440048 z^5 + 395232 z^6 - 35648 z^7 + 1024 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]