Higher Apéry-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator
نویسنده
چکیده
A generalization of the Apéry-like numbers, which is used to describe the special values ζQ(2) and ζQ(3) of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a recurrence relation for them, which shows a ladder structure among them. Further, we consider the ‘rational part’ of the higher Apéry-like numbers. We discuss several kinds of congruence relations among them, which are regarded as an analogue of the ones among Apéry numbers.
منابع مشابه
Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators
We derive an expression for the value ζQ(3) of the spectral zeta function ζQ(s) studied in [10, 11] for the non-commutative harmonic oscillator defined in [17] using a Gaussian hypergeometric function. In this study, two sequences of rational numbers, denoted J̃2(n) and J̃3(n), which can be regarded as analogues of the Apéry numbers, naturally arise and play a key role in obtaining the expression...
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