Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions
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Publication:2130799
DOI10.3934/math.2021438zbMath1484.11084OpenAlexW3186085134MaRDI QIDQ2130799
Feng Qi, Dongkyu Lim, Bai-Ni Guo
Publication date: 25 April 2022
Published in: AIMS Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/math.2021438
series expansionpowerseries representationspecial valueclosed-form formulaarcsinegeneral expressiongeneralized logsine functionsecond kind Bell polynomials
Polynomials in number theory (11C08) Special sequences and polynomials (11B83) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Denjoy and Perron integrals, other special integrals (26A39) Special polynomials in general fields (12E10) Exponential and trigonometric functions (33B10)
Related Items
MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function, Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers, Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials, Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers, Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi, Unnamed Item
Uses Software
Cites Work
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- Special values of the Bell polynomials of the second kind for some sequences and functions
- Integral representations and properties of Stirling numbers of the first kind
- Approximation by special values of harmonic zeta function and log-sine integrals
- LOG-SINE AND LOG-COSINE INTEGRALS
- Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
- Generalized log sine integrals and the Mordell-Tornheim zeta values
- Explicit evaluations of some families of log-sine and log-cosine integrals
- Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions
- Log-Sine integrals involving series associated with the zeta function and polylogarithms
- Closed formulas and identities on the Bell polynomials and falling factorials.
- Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals
- [https://portal.mardi4nfdi.de/wiki/Publication:3671493 On the Integral � π/2 0 log n cosx log p sinx dx]
- Interesting Series Involving the Central Binomial Coefficient
- Closed formulas for special bell polynomials by Stirling numbers and associate Stirling numbers
- Sharp Wilker and Huygens type inequalities for trigonometric and inverse trigonometric functions
- SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS
- A diagonal recurrence relation for the Stirling numbers of the first kind
- Notes on two kinds of special values for the Bell polynomials of the second kind
- Special values of generalized log-sine integrals
- A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind
- Closed Forms: What They Are and Why We Care
- Diagonal recurrence relations for the Stirling numbers of the first kind
- Some Interesting Series Resulting from a Certain MacLaurin Expansion
- New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams
- On rapidly convergent series expressions for zeta- and \(L\)-values, and log sine integrals
