Some properties of the divided difference of psi and polygamma functions
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DOI: 10.1016/j.jmaa.2017.05.081
Abstract: Abstract Let ψ n = ( − 1 ) n − 1 ψ ( n ) for n ≥ 0 , where ψ ( n ) stands for the psi and polygamma functions. For p… read more here.
Keywords: psi polygamma; difference psi; divided difference; properties divided ... See more keywords
Complete monotonicity involving the divided difference of polygamma functions
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DOI: 10.2298/aadm210630007y
Abstract: For r, s ? R and ? = min {r, s}, let D[x + r, x + s; ?n?1] ? ??n (x) be the divided difference of the functions ?n?1 = (?1)n ?(n?1) (n ?… read more here.
Keywords: monotonicity involving; complete monotonicity; divided difference; polygamma functions ... See more keywords
Generalized the q-Digamma and the q-Polygamma Functions via Neutrices
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DOI: 10.2298/fil1705475s
Abstract: The $q$-digamma function $\psi_q(x)$ and the $q$-polygamma functions $\psi^{(r)}_q(x),~r\in\N$ are defined for all $x>0$ and $0 read more here.
Keywords: digamma polygamma; via neutrices; generalized digamma; polygamma functions ... See more keywords
Some New Inequalities for the Gamma and Polygamma Functions
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DOI: 10.3390/sym17040595
Abstract: In this paper, we present some new symmetric bounds for the gamma and polygamma functions. For this goal, we present two functions involving gamma and polygamma functions and we investigate their complete monotonicity. Also, we… read more here.
Keywords: inequalities gamma; new inequalities; polygamma functions; gamma polygamma ... See more keywords