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In mathematics, Pfaffian functions are a certain class of functions introduced by Askold Georgevich Khovanskiǐ in the 1970s. They are named after German mathematician Johann Pfaff. ==Basic definition== Some functions, when differentiated, give a result which can be written in terms of the original function. Perhaps the simplest example is the exponential function, ''f''(''x'') = ''e''''x''. If we differentiate this function we get ''ex'' again, that is : Another example of a function like this is the reciprocal function, ''g''(''x'') = 1/''x''. If we differentiate this function we will see that : Other functions may not have the above property, but their derivative may be written in terms of functions like those above. For example, if we take the function ''h''(''x'') = ''e''''x''log(''x'') then we see : Functions like these form the links in a so-called Pfaffian chain. Such a chain is a sequence of functions, say ''f''1, ''f''2, ''f''3, etc., with the property that if we differentiate any of the functions in this chain then the result can be written in terms of the function itself and all the functions preceding it in the chain (specifically as a polynomial in those functions and the variables involved). So with the functions above we have that ''f'', ''g'', ''h'' is a Pfaffian chain. A Pfaffian function is then just a polynomial in the functions appearing in a Pfaffian chain and the function argument. So with the Pfaffian chain just mentioned, functions such as ''F''(''x'') = ''x''3''f''(''x'')2 − 2''g''(''x'')''h''(''x'') are Pfaffian. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pfaffian function」の詳細全文を読む スポンサード リンク
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