Lectures On the Theory of Elliptic Functions
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In our eReader you can find the full English version of the book. Read Lectures On the Theory of Elliptic Functions Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Lectures On the Theory of Elliptic Functions
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To quickly assess the difficulty of the text, read a short excerpt:
. , may be determined at once.
For example, let n = 4 and for brevity put At = 4 l a z . If the multiple arcs are replaced by the powers of the cosine, we have cos + 4 a i cos 3 + 16 a 2 cos 5 + 64 a 3 cos"0 + 256 a 4 cos 9 = cos + ai(cos 3 + 3 cos 0) + a 2 (cos 5 + 5 cos 3 + 10 cos 0) + a 3 (cos 7 + 7 cos 5 4- 21 cos 3 + 35 cos 0) + a 4 (cos 9 + 9 cos 7 + 36 cos 5 4- 84 cos 3 -4- 126 cos 0) = cos 9 + 4 a! cos 5 4- 16 a 2 cos + 64 a 3 cos 3 + 256 a 4 cos 7 0.
254 THEOEY OF ELLIPTIC FUNCTIONS.
W...e thus have among the a s the five equations * 1 - a 4, 4i = a 2 + 7a 3 + 36 a 4, 16 a 2 - 1 + 3 ai + 10 a 2 + 35 a 3 + 126 a 4, 64 a 3 = a! + 5 a 2 + 21 a 3 + 84 a 4, 256 #4 = #3 + 9 a 4 .
Since the sum of these equations leads to an identity, we may omit any one of them, say the third; and from the other four we have i= 922, a 2 = 1923, o 3 = 247, a 4 = 1, which agree with the above results of Gudermann. Since the coefficients of dn(u, k) are at once deduced from those of cn(u, k); while those of sn(u, k) may be obtained from the formula sn (u, k) = cn(u, k) dn(u, k).
What to read after Lectures On the Theory of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. , may be determined at once.
For example, let n = 4 and for brevity put At = 4 l a z . If the multiple arcs are replaced by the powers of the cosine, we have cos + 4 a i cos 3 + 16 a 2 cos 5 + 64 a 3 cos"0 + 256 a 4 cos 9 = cos + ai(cos 3 + 3 cos 0) + a 2 (cos 5 + 5 cos 3 + 10 cos 0) + a 3 (cos 7 + 7 cos 5 4- 21 cos 3 + 35 cos 0) + a 4 (cos 9 + 9 cos 7 + 36 cos 5 4- 84 cos 3 -4- 126 cos 0) = cos 9 + 4 a! cos 5 4- 16 a 2 cos + 64 a 3 cos 3 + 256 a 4 cos 7 0.
254 THEOEY OF ELLIPTIC FUNCTIONS.
W...e thus have among the a s the five equations * 1 - a 4, 4i = a 2 + 7a 3 + 36 a 4, 16 a 2 - 1 + 3 ai + 10 a 2 + 35 a 3 + 126 a 4, 64 a 3 = a! + 5 a 2 + 21 a 3 + 84 a 4, 256 #4 = #3 + 9 a 4 .
Since the sum of these equations leads to an identity, we may omit any one of them, say the third; and from the other four we have i= 922, a 2 = 1923, o 3 = 247, a 4 = 1, which agree with the above results of Gudermann. Since the coefficients of dn(u, k) are at once deduced from those of cn(u, k); while those of sn(u, k) may be obtained from the formula sn (u, k) = cn(u, k) dn(u, k).
What to read after Lectures On the Theory of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
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