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Notations

♦*♦ABCDEFGHIJKLMNOPQRSTUVWXYZ
!
factorial (as in n!); Common Notations and Definitions
!q
q-factorial (as in n!q); 5.18.2
!!
double factorial (as in n!!); Common Notations and Definitions
ab: vector dot (or scalar) product; 1.6.2
*
f*g: convolution for Laplace transforms; 1.14.30
*
f*g: convolution for Mellin transforms; 1.14.39
*
f*g: convolution product; 2.6.34
*
f*g: convolution for Fourier transforms; 1.14.5
×
G×H: Cartesian product of groups G and H; §23.1
×
a×b: vector cross product; 1.6.9
implies; Common Notations and Definitions
is equivalent to; Common Notations and Definitions
/
S1/S2: set of all elements of S1 modulo elements of S2; §21.1
\
set subtraction; Common Notations and Definitions
asymptotic equality; 2.1.1
backward difference operator; §3.10(iii)
del operator; 1.6.19
2
Laplacian; §1.5(ii)
2
Laplacian for polar coordinates; §1.5(ii)
2
Laplacian for cylindrical coordinates; §1.5(ii)
2
Laplacian for spherical coordinates; §1.5(ii)
f
gradient of differentiable scalar function f; 1.6.20
F
divergence of vector-valued function F; 1.6.21
×F
curl of vector-valued function F; 1.6.22
integral; §1.4(iv)
ab
Cauchy principal value; 1.4.24
a(b+)
loop integral in : path begins at a, encircles b once in the positive sense, and returns to a.; §5.9(i)
P(1+,0+,1-,0-)
Pochhammer’s loop integral; §5.12
dqx
q-integral; §17.2(v)
z¯
complex conjugate; 1.9.11
|z|
modulus (or absolute value); 1.9.7
a
magnitude of vector; 1.6.3
Ap
p-norm of a matrix; §3.2(iii)
x2
Euclidean norm of a vector; §3.2(iii)
x
infinity (or maximum) norm of a vector; §3.2(iii)
xp
p-norm of a vector; §3.2(iii)
f(c+)
limit on right (or from above); 1.4.1
f(c-)
limit on left (or from below); 1.4.3
f[n](z)
nth q-derivative; §17.2(iv)
xn¯
falling factorial; §26.1
xn¯
rising factorial; §26.1
b0+a1b1+a2b2+
continued fraction; §1.12(i)
(a)n
Pochhammer’s symbol; §5.2(iii)
(z-1)!=Γ(z)
alternative notation; §5.1
(with Γ(z): gamma function)
(m,n)
greatest common divisor (gcd); §27.1
(a,b)
open interval; Common Notations and Definitions
(a,b]
half-closed interval; Common Notations and Definitions
(n|P)
Jacobi symbol; §27.9
(n|p)
Legendre symbol; §27.9
(a;q)n
q-Pochhammer (or q-shifted factorial); §17.2(i)
(a1,a2,,ar;q)n
multiple q-Pochhammer symbol; §17.2(i)
(a,z)!=γ(a+1,z)
notation used by Dingle (1973); §8.1
(with γ(a,z): incomplete gamma function)
(j1m1j2m2|j1j2j3-m3)
Clebsch–Gordan coefficient; §34.1
(mn)
binomial coefficient; 1.2.1
(n1+n2++nkn1,n2,,nk)
multinomial coefficient; §26.4(i)
(j1j2j3m1m2m3)
3j symbol; 34.2.4
Λ,ϕ
distribution; §1.16(i)
f,ϕ
tempered distribution; 2.6.11
δ,ϕ
Dirac delta distribution; §1.16(iii)
nk
Eulerian number; §26.14(i)
x
floor of x; Common Notations and Definitions
x
ceiling of x; Common Notations and Definitions
[z0,z1,,zn]
divided difference; §3.3(iii)
[a]κ
partitional shifted factorial; 35.4.1
[a,b)
half-closed interval; Common Notations and Definitions
[a,b]
closed interval; Common Notations and Definitions
[p/q]f
Padé approximant; §3.11(iv)
[a,z]!=Γ(a+1,z)
notation used by Dingle (1973); §8.1
(with Γ(a,z): incomplete gamma function)
[nk]
Stirling cycle number; §26.13
[nm]q
q-binomial coefficient (or Gaussian polynomial); 17.2.27
[a1+a2++ana1,a2,,an]q
q-multinomial coefficient; §26.16
[nk]=(-1)n-ks(n,k)
notation used by Knuth (1992), Graham et al. (1994), Rosen et al. (2000); §26.1
(with s(n,k): Stirling number of the first kind)
{}
sequence, asymptotic sequence (or scale), or enumerable set; §2.1(v)
{z,ζ}
Schwarzian derivative; 1.13.20
{nk}=S(n,k)
notation used by Knuth (1992), Graham et al. (1994), Rosen et al. (2000); §26.1
(with S(n,k): Stirling number of the second kind)
{j1j2j3l1l2l3}
6j symbol; 34.4.1
{j11j12j13j21j22j23j31j32j33}
9j symbol; 34.6.1