関数L: x→∫^x_1 dt/t(x>0)と,その逆関数について
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概要
- 論文の詳細を見る
We needed the calculation of enomous numbers while we were studying the movement of the planet. At the same time we found it very necessary to calculate those numbers very easily. Napier (1550-1617) invented the way of calculation by means of logarithm which he showed in his thesis of Mirifici logarithmorum canonis descriotio published in 1614. At the 18th century after his invention, Euler (1707-1783) defined exponential function. Moreover, he defined logarithmic function as the inverse function of exponential function. He is known to have unified logarithm theoretically. This thesis is concerned with the other way. It proves theoretically the relationship of correspondence between the quantity varying with geometrical series and the one varying with arithmetical series in the phenomenal world. It defines logarithmic function with fluxional analysis as a mathematical model of elementary transcendental functions. It further defines exponential function as inverse function and shows the characteristics of these functions. Hilbert (1862-1943) said: Mathematics is not to pursue the truth in correspondence with the phenomenal world. It only draws the conclusion formally on the supposition that any contradiction should never rise. It never has any purpose except that it makes "abstract theory." Nevertheless, if mathematics is confined in its world, it can not make its progress but brush its technic like the native mathematics of Japan. It is understandable that mere suppositions take place of the axioms of mathematics. But the suppositions seem to be more powerful when we can raise them on the fertile ground of natural science in the phenomenal world. Therefore this thesis explains in the section of the phenomenal world, in the section of the logarithmic function and in the section of the exponential function.
- 名古屋女子大学の論文
- 1984-03-31