The tensor functions , , , and can have unit values at infinity:
The tensor functions , , , , and have the following values for some specialized variables:
and are nonanalytical functions defined over . Their possible values are and .
and are nonanalytical functions defined over . Their possible values are and .
is a nonanalytical function, defined over the set of tuples of complex numbers with possible values .
The tensor functions , , , , and do not have periodicity.
The tensor functions , , , and are even functions:
The tensor functions , , and have permutation symmetry, for example:
The discrete delta function and Kronecker delta function have the following integral representations along the interval and unit circle :
The tensor functions , , , , and satisfy various identities, for example:
The tensor functions , , , , and have the following complex characteristics:
Differentiation of the tensor functions and can be provided by the following formulas:
Fractional integro‐differentiation of the tensor functions and can be provided by the following formulas:
Indefinite integration of the tensor functions and can be provided by the following formulas:
The following relations represent the sifting properties of the Kronecker and discrete delta functions:
There exist various formulas including finite summation of signature , for example:
