, List of Symbols
[a,b] closed interval : a x b.
(a,b) open interval : a<x<b.
|a,b| any interval with end pointsaand b.
n! factorial, n! = 1 · 2 · 3 · ...· n.
(2n)!! double factorial, (2n)!! = 2 · 4 · 6 · · · (2n− 2)(2n) = 2n n!
(2n + 1)!! = 1 · 3 · 5 · · · (2n− 1)(2n+ 1) = (2n+ 1)!/2n n! (double
factorial) lnx = logex, natural logarithm, that is the logarithm with
base e.
nk = n(n− 1)...,(n− k+ 1) (falling factorial).
n nk n! binomial coefficient.
= =
k k! k !(n − x)!
n
Dn(fg) = n Dn−rf r ), Leibniz formula, D = d/dx.
( Dg
r=0
r
D the derivative operator.
x
sin t
Si(x) t.
sine integral: 0 t d
∞
cos t
Ci(x) cosine integral: − dt.
1 1 +x x t
arctanh x = ln
2 1 − , hyperbolic arctangent.
x
I the identity matrix.
tr (A) trace of a matrix A.
det (A) determinant of a matrix A, §7.2.
AT transpose of a matrix A (also denoted as A′).
A∗ or AH, adjoint of a matrix A.
ODE Ordinary Differential Equation.
PDE Partial Differential Equation.
y˙ = dy/dt, derivative with respect to time variable t.
j unit pure imaginary vector on the complex plane C: j2 = −1.
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[a,b] closed interval : a x b.
(a,b) open interval : a<x<b.
|a,b| any interval with end pointsaand b.
n! factorial, n! = 1 · 2 · 3 · ...· n.
(2n)!! double factorial, (2n)!! = 2 · 4 · 6 · · · (2n− 2)(2n) = 2n n!
(2n + 1)!! = 1 · 3 · 5 · · · (2n− 1)(2n+ 1) = (2n+ 1)!/2n n! (double
factorial) lnx = logex, natural logarithm, that is the logarithm with
base e.
nk = n(n− 1)...,(n− k+ 1) (falling factorial).
n nk n! binomial coefficient.
= =
k k! k !(n − x)!
n
Dn(fg) = n Dn−rf r ), Leibniz formula, D = d/dx.
( Dg
r=0
r
D the derivative operator.
x
sin t
Si(x) t.
sine integral: 0 t d
∞
cos t
Ci(x) cosine integral: − dt.
1 1 +x x t
arctanh x = ln
2 1 − , hyperbolic arctangent.
x
I the identity matrix.
tr (A) trace of a matrix A.
det (A) determinant of a matrix A, §7.2.
AT transpose of a matrix A (also denoted as A′).
A∗ or AH, adjoint of a matrix A.
ODE Ordinary Differential Equation.
PDE Partial Differential Equation.
y˙ = dy/dt, derivative with respect to time variable t.
j unit pure imaginary vector on the complex plane C: j2 = −1.
iii
