Cayley's problem
Petek, Peter
Applications of Mathematics, Tome 35 (1990), p. 140-146 / Harvested from Czech Digital Mathematics Library
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Newton's method for computation of a square root yields a difference equation which can be solved using the hyperbolic cotangent function. For the computation of the third root Newton's sequence presents a harder problem, which already Cayley was trying to solve. In the present paper two mutually inverse functions are defined in order to solve the difference equation, instead of the hyperbolic cotangent and its inverse. Several coefficients in the expansion around the fixed points are obtained, and the expansions are glued together in the region of overlapping.

Publié le : 1990-01-01
Classification:  39A10,  58C30,  58F08,  65H05,  65Q05 
@article{104395,
     author = {Peter Petek},
     title = {Cayley's problem},
     journal = {Applications of Mathematics},
     volume = {35},
     year = {1990},
     pages = {140-146},
     zbl = {0709.39001},
     mrnumber = {1042849},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104395}
}

Petek, Peter. Cayley's problem. Applications of Mathematics, Tome 35 (1990) pp. 140-146. http://gdmltest.u-ga.fr/item/104395/

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