Notations *
: factorial; Common Notations and Definitions
:
-factorial; §5.18(i)
: double factorial; Common Notations and Definitions
: vector dot (or scalar) product; (1.6.2)
: convolution for Fourier transforms; (1.14.5)
: convolution for Laplace transforms; (1.14.30)
: convolution product; (2.6.34)
: convolution for Mellin transforms; (1.14.39)
: Cartesian product of groups
and
; §23.1
: vector cross product; (1.6.9)
- implies; Common Notations and Definitions
- is equivalent to; Common Notations and Definitions
: set of all elements of
modulo elements of
; §21.1
- set subtraction; Common Notations and Definitions
- asymptotic equality; (2.1.1)
- backward difference operator; ¶ ‣ §3.10(iii)
- del operator; (1.6.19)
- Laplacian for polar coordinates; ¶ ‣ §1.5(ii)
- Laplacian; ¶ ‣ §1.5(ii)
- Laplacian for spherical coordinates; ¶ ‣ §1.5(ii)
- Laplacian for cylindrical coordinates; ¶ ‣ §1.5(ii)
- gradient of differentiable scalar function
; (1.6.20)
- divergence of vector-valued function
; (1.6.21)
- curl of vector-valued function
; (1.6.22)
- integral; §1.4(iv)
- Cauchy principal value; (1.4.24)
- loop integral in
: path begins at
, encircles
once in the positive sense, and returns to
.; ¶ ‣ §5.9(i)
- Pochhammer’s loop integral; ¶ ‣ §5.12
-integral; §17.2(v)
- complex conjugate; (1.9.11)
- modulus (or absolute value); (1.9.7)
- magnitude of vector; (1.6.3)
-norm of a matrix; §3.2(iii)
- Euclidean norm of a vector; §3.2(iii)
- infinity (or maximum) norm of a vector; §3.2(iii)
-norm of a vector; §3.2(iii)
- limit on right (or from above); (1.4.1)
- limit on left (or from below); (1.4.3)
th
-derivative; §17.2(iv)
- falling factorial; ¶ ‣ §26.1
- rising factorial; ¶ ‣ §26.1
- continued fraction; §1.12(i)
- Pochhammer’s symbol; §5.2(iii)
- alternative notation; §5.1
(with: gamma function)
- open interval; Common Notations and Definitions
- half-closed interval; Common Notations and Definitions
- Jacobi symbol; §27.9
- Legendre symbol; §27.9
-factorial (or
-shifted factorial); §17.2(i)
-factorial (or
-shifted factorial); §5.18(i)
-shifted factorial (generalized); §17.2(i)
-shifted factorial; §17.2(i)
- multiple
-shifted factorial; §17.2(i)
- multiple
-shifted factorial; §17.2(i)
- notation used by Dingle (1973); §8.1
(with: incomplete gamma function)
- Clebsch–Gordan coefficient; §34.1
- binomial coefficient; §26.3(i)
- binomial coefficient; (1.2.1)
- multinomial coefficient; §26.4(i)
symbol; (34.2.4)
- tempered distribution; (2.6.11)
- distribution; §1.16(i)
- Dirac delta distribution; §1.16(iii)
- Eulerian number; §26.14(i)
- floor of
; Common Notations and Definitions
- ceiling of
; Common Notations and Definitions
- divided difference; §3.3(iii)
- partitional shifted factorial; (35.4.1)
- half-closed interval; Common Notations and Definitions
- closed interval; Common Notations and Definitions
- Padé approximant; §3.11(iv)
- notation used by Dingle (1973); §8.1
(with: incomplete gamma function)
- Stirling cycle number; §26.13
-binomial coefficient (or Gaussian polynomial); (17.2.27)
-binomial coefficient (or Gaussian polynomial); §26.9(ii)
- notation used by Knuth (1992), Graham et al. (1994), Rosen et al. (2000); ¶ ‣ §26.1
(with: Stirling number of the first kind)
-multinomial coefficient; §26.16
- sequence, asymptotic sequence (or scale), or enumerable set; §2.1(v)
- Schwarzian derivative; (1.13.20)
- notation used by Knuth (1992), Graham et al. (1994), Rosen et al. (2000); ¶ ‣ §26.1
(with: Stirling number of the second kind)
symbol; (34.4.1)
symbol; (34.6.1)