Notations

STILL UNDER CONSTRUCTION

Numbers, Variables and Functions

Domains and Domain Membership

Types of Variables

Set Membership

Types of Functions

Logical Operators and Conditionals

Logical Operators

Conditionals, Equality and Ordering Operators

Operations

Domain and Range

Branch Cuts and Points, Singularities and Discontinuities

Asymptotics and Series

Summations

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Differentiations

Fractional Integro-Differentiations

Integrations

Let for the bounded open contour L=L(a,b) the variable t is moving in positive direction: from the end a to b, the arbitrary points (Subscript[t, k])∈L are numerated in corresponding order ((Subscript[t, 0])==a, (Subscript[t, 1]),…,(Subscript[t, n])==b). Devided on L((Subscript[t, k-1]),(Subscript[t, k])).Then (∫_L)f(t)dt==(lim_(Δ->0)) ((∑_(k=1)^n)f((Subscript[τ, k])) |(Subscript[t, k])-(Subscript[t, k-1])|)/;(Subscript[τ, k])∈L((Subscript[t, k-1]),(Subscript[t, k]))∧Δ==max(|(Subscript[t, 1])-(Subscript[t, 0])|,|(Subscript[t, 2])-(Subscript[t, 1])|,…,|(Subscript[t, n])-(Subscript[t, n-1])|)∧f(τ)∈(C^0)(L(a,b))

For closed contour L (like circle |t|==1) the above procedure can be applied when b is taken on L near point a and then (∫_L)f(t)dt==(lim_(b->a)) (∫_(L(a,b)))f(t)dt

For non-bounded contour L with finite end a the above procedure can be applied when b is taken on L near point (OverTilde[∞]) and then (∫_L)f(t)dt==(∫_(L(a,(OverTilde[∞]))))f(t)dt==(lim_(b->(OverTilde[∞]))) (∫_(L(a,b)))f(t)dt

For non-bounded contour L with both infinite ends (like for the special contour ℒ which is used in definition of Meijer G function) by definition (∫_L)f(t)dt==(∫_(Subscript[L, 1]))f(t)dt-(∫_(Subscript[L, 2]))f(t)dt where L is devided on two contours (Subscript[L, 1])and (Subscript[L, 2])by arbitrary finite poinf a∈L and directions of L and (Subscript[L, 1])are coincide.

Integral Transforms

Limits

Continued Fractions

Matrices and Determinants

Symbols

Functions in Alphabetical Order

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H

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L

M

N

P

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T

U

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Greek

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