Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1533)

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=-3/2

http://functions.wolfram.com/07.25.03.1533.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(3/2), 4}, z] == (1/(6891885 z)) (4 E^(z/2) (654885 + 1704780 z + 2869020 z^2 + 10264248 z^3 - 28314624 z^4 + 14595072 z^5 - 2383872 z^6 + 114688 z^7) BesselI[0, z/2]) - (1/(6891885 z^2)) (4 E^(z/2) (2619540 - 72765 z - 790020 z^2 - 1229868 z^3 - 2406216 z^4 - 16951296 z^5 + 12383232 z^6 - 2269184 z^7 + 114688 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]