### A Note on the Recurrence Theorem

Filipczak, Tomasz (2015-12-07T12:09:00Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Filipczak, Tomasz (2015-12-07T12:09:00Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Four-term recurrence relations for hypergeometric functions of the second order are deduced from generating functions involving elementary functions. Generalisations are indicated and an example is given of a five-term recurrence for the confluent hypergeometric function.

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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.

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