 Fi(x, y, 2Q = 0, which for x = x0, y = y6 has a zero root x. = 0. If this is a simple root, we derive from it a development for x — x0 in powers of y — y0 beginning with a term of at least the second degree. Conversely, the point...  A Course in Mathematical Analysis - Page 195by Edouard Goursat - 1917Full view - About this book
 | Edouard Goursat - Calculus - 1917 - 309 pages
...integral considered corresponds to the value C = 0 of the arbitrary constant. If for x = X Q , y = y 0 a root of the equation (41') is infinite, it will...(41) is replaced by an equation of the same form, Ffa, y, x'y) = 0, which for x — X Q , y = ?/ 0 has a zero root x 1 = 0. If this is a simple root,... | |
 | Edouard Goursat - Calculus - 1917 - 316 pages
...considered corresponds to the value C = 0 of the arbitrary constant. If for x = x0, y = 2/oa root of tne equation (41') is infinite, it will suffice to regard...replaced by an equation of the same form, F^x, y, x'f) = 0, which for x = a;0, y = y0 has a zero root x' = 0. If this is a simple root, we derive from... | |
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