Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1487)

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/07.25.03.1487.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(7/2), 4}, z] == (1/(80405325 z)) (4 E^(z/2) (31216185 + 14698530 z + 5987520 z^2 + 2909760 z^3 + 2119680 z^4 + 4165632 z^5 - 6815744 z^6 + 917504 z^7) BesselI[0, z/2]) - (1/(80405325 z^2)) (4 E^(z/2) (124864740 - 21611205 z - 10914750 z^2 - 4327680 z^3 - 1944000 z^4 - 1185792 z^5 - 1273856 z^6 - 5898240 z^7 + 917504 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]