Name of function

Name of function is sequence of letters (and sometimes, also numerical digits) used to identify the mathematical functions.

Name is important to deal with any object or subject, in order to distinguish it/him/her from other element of the same set. For functions, the name is especially important because it allows to denote the complicated expression or article in TORI with few digits.

The name can be used to find description or implementation of a function in TORI or any other database.

The name can be used in the call of function in a program, code, that is supposed to be translated or interpreted by some appropriate software. In TORI, most of codes refer to C++ language, but some are also in Mathematica. Those in Maple (See, for example, Maple and Tea) or in other languages may also appear.

Policy of names in TORI
Usually, the names of functions use the ascii characters, namely, letters and, in exceptional cases, cifers. (Cifer is one of the following symbols: 0,1,2,3,4,5,6,7,8,9), but the first character must be letter.

The name should not contain spacebars, parenthesis nor special characters. For example, use of sequence of characters "f(x)" as name of function is wrong. For a local name that has specific meaning only within some formula, paragraph or article, the function may be called just f, and the parenthesis after it are used to indicate the argument, and not to identify the function. For example, expressions like \(~f(x)=\int \exp(ikx) f(k) {\rm d}{k}~\) are nonsense, similar to writing \(\int \frac{f(x)}{\mathrm d x}\).

Local name
The local names have specific meaning within one of few formulas, one or few sections, and have other meaning in other formulas.

Usually, such local name consist of a single letter of the Latin alphabet, but letters from other alphabets can be used too, under conditions, that they are correctly treated by the Latex interpreter, used in TORI. For example, expression \(\displaystyle ~ {Ю}(x)= \int_{A}^{Я} \frac{鳥(\alpha)}{魚(x\!+\!\alpha)} \mathrm d \alpha~\) seems to be recognized, although there may be some problem with Italication of non-English characters. Such extravagant names of variables and names of functions can be used in the emergency cases, when all simple letters of the Latin and Greek alphabet already mean other objects, and the urgent help from the Russian and Japanese cultures is essential. However, at the translation to C++, such an expression may cause confusions, to, if possible, the characters from the English alphabet are strongly recommended.

If the name of function is single letter, it may appear with Italics font.

Names consisting of more characters, must be with Roman font. For example, \(arccos(x)\) means product of \(a,r,c^2,o\) and function \(s\) evaluated at artument \(x\), but never \(\arccos(x)\). If the letters of a name of a function appear with Italics, this is just error, misprint, that should be reported and corrected.

Global names
Some names go through several articles with the same meaning. In particular, this refers to the names of special functions.

Several names, mainly those of the elementary functions may use the lowercase letters, as \(\sin\), \(\exp\), \(\mathrm{erf}\). Especially this applies to the names of functions that are already implemented in the most of the C++ compilers. There are few exceptions: tet, arctet, zex; mainly for the functions that are believed to have deep fundamental meaning. All other name should begin with Capital letter. In TORI, in the article, dedicated to some function and named after this function, the first letter is automatically capitalized.

If possible, the global name should coincide with that used in Matematica software, in order to use expression from TORI in the Mathematica codes without any modification. (However, the parenthesis after the name of a function should be replaced from (~) to [~]; \(~\ln~\) should be replaced to Log and so on.)

If the function yet has no established name (and not implemented in Matehmatica), or if this name is not found in time, the name of a colleague who is somehow related with the function is used. For example, the name for the Tania function had been given before to realize that it is just WrightOmega with argument displaced for unity.

The name can be created from the object, that was not considered as a function, for example, the Logistic sequence. This sequence is generalized and interpreted a holomorphic function of complex variable.

The use of non–English characters in the global names is not recommended at all. For example, the WrightOmega is not written as Wright\(\Omega\); perhaps, some Sakana function (as soon as it will be requested, implemented, described and loaded) will be called \(\mathrm{Sakana}\) and not \(魚\).

In general, the new global names are supposed to consist of English letters and to begin with capital letter.

Suggestions
Any critics of the names of functions used in TORI should be supplied with suggestions, how is it better to call some function.

Suggestions of names like "Function_Used_in_Article_By_Brueck_et_All_[13]_and_denoted_there_with_letter_f" will not be considered; the advisers will be suggested to write some formulas where such a function appears several times and realize how ugly is such an expression.

Keywords
ArcTania, AbelFactorial, Tania function, Doya function, Factorial, Logistic sequence, Shoka function, SuperFactorial, Tetration, LambertW, WrightOmega, Zex