Concrete Mathematics(2nd Edition) - A Note on Notation

lnx

natural logarithm: logex

lgx

binary logarithm: log2x

logx

common logarithm: log10x

⌊x⌋

floor: max{n | n≤x, integer n}

⌈x⌉

ceiling: min{n | n≥x, integer n}

xmody

remainder: x−y⌊x/y⌋

{x}

fractional part: xmod1

∑f(x)δx

indefinite summation

∑baf(x)δx

definite summation

xn−

falling factorial power: x!/(x−n)!

xn¯

rising factorial power: Γ(x+n)/Γ(x)

ni

subfactorial: n!/0!−n!/1!+⋯+(−1)nn!/n!

Rz

real part: x, if z=x+iy

Iz

imaginary part: y, if z=x+iy

Hn

harmonic number: 1/1+⋯+1/n

H(x)n

generalized harmonic number: 1/1x+⋯+1/nx

f(m)(z)

mth derivative of f at z

[nm]

Stirling cycle number (the “first kind”)

{nm}

Striling cycle number (the “second kind”)

⟨nm⟩

Eulerian number

⟨⟨nm⟩⟩

Second order Eulerian number

(am,…,a0)b

radix notation for ∑mk=0akbk

K(a1,…,an)

continuant polynomial

F(a,bc∣∣z)

hypergeometric function

#A

cardinality: number of elements in the set A

[zn]f(z)

coefficient of zn in f(z)

[α..β]

closed interval: the set {x | α≤x≤β}

[m=n]

1 if m=n, otherwise 0∗

[m∖n]

1 if m divides n, otherwise 0∗

[m∖∖n]

1 if m exactly divides n, otherwise 0∗

[m⊥n]

1 if m is relatively prime to n, otherwise 0∗