Green's Functions with Applications, 2nd Edition

Definitions of the Most Commonly Used Functions

Function	Definition
$\delta \left(t-a\right)$	$=\{\begin{array}{cc}\infty ,& t=a,\\ 0,& t\ne a,\end{array}{\displaystyle {\int }_{-\infty }^{\infty }\delta \left(t-a\right)dt=1}$
$H\left(t-a\right)$	$=\{\begin{array}{cc}1,& t>a,\\ 0,& t<a,\end{array}a\ge 0$
In(x)	modified Bessel function of the first kind and order n
Jn(x)	Bessel function of the first kind and order n
Kn(x)	modified Bessel function of the second kind and order n
Pn(x)	Legendre polynomial of order n
r<	= min(r, ρ)
r>	= max(r, ρ)
x<	= min(x, ξ)
x>	= max(x, ξ)
Yn(x)	Bessel function of the second kind and order n
y<	=min(y, η)
y>	=max(y, η)
z<	min(z,ζ)
z>	max(z,ζ)