The Mathematical And Other Writings of Robert Leslie Ellis Microform
The Mathematical And Other Writings of Robert Leslie Ellis Microform
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Jacobi demonstrates is not less remarkable. It is that the combination of the first and second real transformations gives a formula for the multiplication of the original integral, or, in other words, that the modulus of the integral which results from this double transformation is the same as that of the original integral, so that the two integrals differ only in their amplitudes. Of this theorem he had in the earlier part of the work proved some particular cases*.
After fully developing this ...part of the subject, he next treats of the nature of the modular equation, and shows that it possesses several remarkable properties. One is, that all modular equations, of whatever order, are particular integrals of a differential equation of the third order, of which the general integral . Can be expressed by means of elliptic tran- scendents.
16. We now enter on the second great division of M. Jacobi's researches, the evolution of elliptic functions.
* It may be shown that if we pass from k to X by the first transformation, we can pass from A/I - X 2 to A/I -& 2 also by the first transformation.
What to read after The Mathematical And Other Writings of Robert Leslie Ellis Microform?
You can find similar books in the "Read Also" column, or choose other free books by Robert Leslie Ellis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Jacobi demonstrates is not less remarkable. It is that the combination of the first and second real transformations gives a formula for the multiplication of the original integral, or, in other words, that the modulus of the integral which results from this double transformation is the same as that of the original integral, so that the two integrals differ only in their amplitudes. Of this theorem he had in the earlier part of the work proved some particular cases*.
After fully developing this ...part of the subject, he next treats of the nature of the modular equation, and shows that it possesses several remarkable properties. One is, that all modular equations, of whatever order, are particular integrals of a differential equation of the third order, of which the general integral . Can be expressed by means of elliptic tran- scendents.
16. We now enter on the second great division of M. Jacobi's researches, the evolution of elliptic functions.
* It may be shown that if we pass from k to X by the first transformation, we can pass from A/I - X 2 to A/I -& 2 also by the first transformation.
What to read after The Mathematical And Other Writings of Robert Leslie Ellis Microform?
You can find similar books in the "Read Also" column, or choose other free books by Robert Leslie Ellis to read onlineMoreLess
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