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A Function which Transforms Certain Graphs into Straight Lines for Simultaneous Solution

Published online by Cambridge University Press:  20 November 2018

Laurence P. Maher Jr.
Laurence P. Maher Jr.*
Affiliation:
Department of Mathematics, North Texas State University, Denton, Texas 76203
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Abstract

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A function M is defined which maps the plane onto a square region in such a way that the planar graphs In, exp, X, —X, 1/X, and all compositions formed from them are transformed into straight lines. One can then solve for their intersections. It also provides a natural definition for the repeated composition of In with itself t times, where t can be a non-integer.

Keywords

Primary; 40A99 sequencesseriessummability—convergence and divergence of infinite limiting processes—miscellaneousSecondary 41A30 Approximations and expansions—approximations by other special function classesInfinite exponential representationBase e infinite exponentialRepeated-composition functionThe m functionThe M functionPlanar graphs′ intersection pointsOrdered commutative group of Int graphs
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 261 - 266
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Barrow, D.F., Infinite exponentials, Amer. Math. Monthly 43 (1936), 150-160.Google Scholar
2. Prestrud, M.B., Hierarchic algebra, Notices Amer. Math. Soc. 8 (1961), 270 Google Scholar
3. Shell, Donald L., On the convergence of infinite exponentials, Proc. Amer. Math. Soc. 13 (1962), 678-681.Google Scholar
4. Thron, W.J., Convergence of infinite exponentials with complex elements, Proc. Amer. Math. Soc. 8 (1957), 1040-1043.Google Scholar