Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9206)

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=1, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=1, b₁=3

http://functions.wolfram.com/07.25.03.9206.01

Input Form

HypergeometricPFQ[{-(5/2), 1}, {3, 5}, z] == (16 (-2 + 3 z))/(21 z^2) - (256 E^(z/2) (-17010 + 33075 z - 20064 z^2 + 4848 z^3 - 480 z^4 + 16 z^5) BesselI[0, z/2])/(2837835 z^2) + (1/(2837835 z^3)) (128 E^(z/2) (-945 - 5670 z + 37938 z^2 - 31776 z^3 + 8784 z^4 - 928 z^5 + 32 z^6) 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]