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Statements

Subject Item

dbr:Monogenic_function

rdfs:label

Monogenic function

rdfs:comment

A monogenic function is a complex function with a single finite derivative. More precisely, a function defined on is called monogenic at , if exists and is finite, with: Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative (monogenic) or infinitely many derivatives (polygenic), with no intermediate cases. Furthermore, a function which is monogenic , is said to be monogenic on , and if is a domain of , then it is analytic as well (The notion of domains can also be generalized in a manner such that functions which are monogenic over non-connected subsets of , can show a weakened form of analyticity)

dcterms:subject

dbc:Mathematical_analysis dbc:Functions_and_mappings

dbo:wikiPageID

66390572

dbo:wikiPageRevisionID

1032162078

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dbr:Analytic_function dbr:Complex_derivative dbc:Functions_and_mappings dbc:Mathematical_analysis dbr:Complex_function dbr:Domain_(mathematical_analysis) dbr:Limit_of_a_function

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dbo:abstract

A monogenic function is a complex function with a single finite derivative. More precisely, a function defined on is called monogenic at , if exists and is finite, with: Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative (monogenic) or infinitely many derivatives (polygenic), with no intermediate cases. Furthermore, a function which is monogenic , is said to be monogenic on , and if is a domain of , then it is analytic as well (The notion of domains can also be generalized in a manner such that functions which are monogenic over non-connected subsets of , can show a weakened form of analyticity)

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wikipedia-en:Monogenic_function?oldid=1032162078&ns=0

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1698

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wikipedia-en:Monogenic_function