DiscreteDelta

DiscreteDelta[n1,n2,]

gives the discrete delta function , equal to 1 if all the ni are zero, and 0 otherwise.

Details

Examples

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Basic Examples  (3)

Evaluate numerically:

Use in sums:

Plot over a subset of the integers:

Scope  (18)

Numerical Evaluation  (4)

Evaluate numerically:

Complex number inputs:

DiscreteDelta always returns an exact result irrespective of the precision of the input:

Evaluate efficiently at high precision:

Specific Values  (4)

Value at zero:

Multiargument form gives 1 when all inputs are zero:

Value at infinity:

Evaluate symbolically:

Visualization  (3)

Plot the single-argument DiscreteDelta using integer-width bins:

Visualize DiscreteDelta over the reals. Except for a jump at , it is indistinguishable from a zero function:

Plot DiscreteDelta in three dimensions:

Function Properties  (3)

DiscreteDelta is defined for all real and complex inputs:

Function range of DiscreteDelta:

The function range for complex values is the same:

TraditionalForm typesetting:

Differentiation and Integration  (4)

First derivative with respect to x:

Series expansion at a generic point:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

More integrals:

Applications  (3)

Use in sums to pick out terms:

Pick out elements:

Patch pointwise values of piecewisedefined functions:

Properties & Relations  (3)

Reduce an equation containing DiscreteDelta:

The support of DiscreteDelta has measure zero:

DiscreteDelta can be represented as a DifferenceRoot:

Possible Issues  (2)

DiscreteDelta can stay unevaluated with numeric arguments:

A larger setting for $MaxExtraPrecision can be needed:

Equality testing of the arguments takes numerical precision into account:

Wolfram Research (1999), DiscreteDelta, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteDelta.html.

Text

Wolfram Research (1999), DiscreteDelta, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteDelta.html.

BibTeX

@misc{reference.wolfram_2021_discretedelta, author="Wolfram Research", title="{DiscreteDelta}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteDelta.html}", note=[Accessed: 29-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_discretedelta, organization={Wolfram Research}, title={DiscreteDelta}, year={1999}, url={https://reference.wolfram.com/language/ref/DiscreteDelta.html}, note=[Accessed: 29-November-2021 ]}

CMS

Wolfram Language. 1999. "DiscreteDelta." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteDelta.html.

APA

Wolfram Language. (1999). DiscreteDelta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteDelta.html