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On the transcendency of the solutions of a special class of functional equations: Corrigendum

Published online by Cambridge University Press:  17 April 2009

Kurt Mahler
Kurt Mahler
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Mr V.E. Hoggatt, Jr, has pointed out an error in the examples of my paper [2], If Fm denotes the mth Fibonacci number, these examples asserted that

is transcendental. This is in fact false, for by a theorem of Good [1],

for it happens that

is a rational and not a transcendental function of z, so that Theorem 1 of my paper cannot be applied. The value of s follows from (1) on putting .

Hence the following changes have to be made in [2].

On p. 390, lines 7 and 10, the case k = 1 must each time be excluded, and in Theorem 2 the two numbers r and s may not be both be 0.

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 477 - 478
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Good, I.J., “A reciprocal series of Fibonacci numbers”, Fibonacci Quart. 12 (1974), 346.Google Scholar
[2]Mahler, Kurt, “On the transcendency of a special class of functional equations”, Bull. Austral. Math. Soc. 13 (1975), 389–410.CrossRefGoogle Scholar