PRACTICAL APPLICATION OF THE FOURIER INTEGRAL 661 



g = epoch ; parameter for the unit impulse. — oo < g < <x> . 



go<g<gi restricts the given coefficient to the indicated Hmits; 



outside these limits the coefficient is zero. 

 ^(g) = coefficient for unit impulse, parameter g. 



H.(.) =,.-«("-') ,.-. + "(»-')(»-2)(''- 3) ^.-,_... 



= Hermite polynomial of order n. 



2 

 Hy^'^\z) = -i-'-^Kyi— iz) = Bessel function of the third kind. 



TT 



2 

 Hy^^\z) = - i''+^Ky{iz) = Bessel function of the third kind. 



TT 



I{z) = imaginary part of s. z = R(z) + il{z). 



Iv{z) = i-'J^{iz). 



j, k, I = integers greater than zero. 



Jviz) = i'Iv{— iz) = Bessel function of the first kind. 



K^z) = ^iri'+^H.^'^iiz). 



m, n = positive integers, including zero. 



dn{ ) = mate of ( ). 



p = ilirf, the imaginary radian frequency. 



r, 5 = reals, positive or zero. 



R{z) = real part of s. s = R{z) + il{z). 



S{z) = S^sm{h^z^)dz = - S{-z). 5(± ^) = ± i. 



^v{x) = lim aDx" exp(— TraV) = z^th singularity function. 



a— >oo 

 ^-n{x) = ( Xi ± ^, [_ ^y \ X"-' + X2.V"-2 H + X„, 0<±X, 



< n. 

 t = time. — CO < / < 00, 



V, w = integers, positive, negative or zero. 



X, y = reals, unrestricted. 



Y = admittance of system for cisoidal oscillation. 



Y,{z) = ^i[W-\z) — i7/i)(2)] = Bessel function of the second 



kind. 



