Closed formulas and identities on the Bell polynomials and falling factorials.
From MaRDI portal
Publication:3303524
DOI10.11575/cdm.v15i1.68111zbMath1471.11102OpenAlexW3119017120MaRDI QIDQ3303524
Bai-Ni Guo, Dongkyu Lim, Feng Qi, Da-Wei Niu
Publication date: 12 August 2020
Full work available at URL: https://cdm.ucalgary.ca/article/download/68111/54030
modified spherical Bessel functionspecial valueFaà di Bruno formulaidentityclosed-form expressionspherical Bessel functionfalling factorialBell polynomial of second kindequivalent expression
Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)
Related Items
Closed formulas for special bell polynomials by Stirling numbers and associate Stirling numbers, Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions, Two Explicit Formulas for Degenerate Peters Numbers and Polynomials, 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, Schur \(m\)-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means, Special values of the Bell polynomials of the second kind for some sequences and functions, Monotonicity and sharp inequalities related to complete \((p,q)\)-elliptic integrals of the first kind, Computation of several Hessenberg determinants, Unnamed Item, 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, Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Explicit expressions for a family of the Bell polynomials and applications
- Derivatives of tangent function and tangent numbers
- Closed formulas for computing higher-order derivatives of functions involving exponential functions
- Some identities and an explicit formula for Bernoulli and Stirling numbers
- Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
- Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
- Some properties of central Delannoy numbers
- 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
- Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function
- Combinatorial Identities for Stirling Numbers