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On a recurrence relation

Published online by Cambridge University Press:  20 January 2009

C. E. Walsh
Affiliation:
34 Chelmsford Road, Ranelagh, Dublin.
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It is proposed here to consider the sequence un determined by the relation

where, in particular,

and initially u1 = θ1. The following is the main result to be proved.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1938

References

page 152 note 1 Knopp, , “Theory and Application of Infinite Series” (1928), 72.Google Scholar

page 152 note 2 Bromwich, , “Infinite Series” (1926), 427.Google Scholar

page 153 note 1 Proc. Edinburgh Math. Soc. (2), 3 (1932), 147150.CrossRefGoogle Scholar

page 154 note 1 Copson and Ferrar, Journal London Math. Soc., 4 (1929), 258264.Google Scholar

page 154 note 2 Bromwich, ibid., 414.

page 154 note 3 Proc. Edinburgh Math. Soc. (2), 3 (1932), 220222.Google Scholar