The ambiguity in the style of writing a function should not be confused with a multivalued function, which can (and should) be defined in a deterministic and unambiguous way. Several special functions still do not have established notations. Usually, the conversion to another notation requires to scale the argument and/or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:
- Sinc function
- Elliptic integral of the third kind; translating elliptic integral form MAPLE to Mathematica, one should replace the second argument to its square, see Talk:Elliptic integral#List_of_notations; dealing with complex values, this may cause problems.
- Exponential integral, page 228 http://www.math.sfu.ca/~cbm/aands/page_228.htm
- Hermite polynomial, page 775 http://www.math.sfu.ca/~cbm/aands/page_775.htm
Read more about Ambiguity: Mathematical Interpretation of Ambiguity, Pedagogic Use of Ambiguous Expressions
Famous quotes containing the word ambiguity:
“There is no greater impediment to the advancement of knowledge than the ambiguity of words.”
—Thomas Reid (1710–1769)
“Unlike the ambiguity of life, the ambiguity of language does reach a limit.”
—Mason Cooley (b. 1927)
“Indeed, it is that ambiguity and ambivalence which often is so puzzling in women—the quality of shifting from child to woman, the seeming helplessness one moment and the utter self-reliance the next that baffle us, that seem most difficult to understand. These are the qualities that make her a mystery, the qualities that provoked Freud to complain, “What does a woman want?””
—Lillian Breslow Rubin (20th century)