Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9781)

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=-5/2, a₂>=-5/2

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

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

http://functions.wolfram.com/07.25.03.9781.01

Input Form

HypergeometricPFQ[{-(5/2), 5/2}, {5/2, 5}, z] == -((32 E^(z/2) (-45 - 75 z - 1500 z^2 + 1260 z^3 - 272 z^4 + 16 z^5) BesselI[0, z/2])/(45045 z^2)) + (32 E^(z/2) (-180 - 300 z - 375 z^2 - 600 z^3 + 1012 z^4 - 256 z^5 + 16 z^6) BesselI[1, z/2])/(45045 z^3)

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]