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Introducing Complex Numbers into Basic Growth Functions (6) : Hypothetic Breakdown of '1' into Complex Numbers and Application to Definite Integral of exp(t) Expanded into Infinite Series

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概要 The definite integral of exp(t) expanded into infinite series included two sets of '1+(-1)' in the caluculation of growth, and each of '1' and '-1' was described using the product of eight complex num...bers. The present study was designed under hypotheses to leave complex numbers by the breakdown of product form in the complex representation of '1', where a minus sigh was given to each of even-numbered pieces of complex number out of eight in order to conserve the value of '1'. This was followed by interting them into the caluclation of growth using exp(t). The results obtained were as folloes. The value of '1' was constructed by the product of complex numbers that were different in part from those used in the primary description, which was caused by giving a minus sign to each of even-numbered (2,4,6,8) pieces of complex number. The hypothetic breakdown of product form in the complex representation of '1' left zero, two or four sorts of complex numbers. The complex numbers were left in more pieces when a minus sign was given to each of the four pieces of complex number than when given to each of two, six, or eight pieces. Inserting complex numbers that were left into exp(t) did not influence the caluclation of growth, suggesting that the definite integral of exp(t) expanded into infinite series was accompanied hypothetically by pair appearances and pair disappearances of complex numbers with their opposites.続きを見る

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登録日 2009.04.22
更新日 2017.02.07