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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:
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