ARTICLE

doi:10.20944/preprints201704.0040.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
Catalan number; integral representation; equivalent relation; application; sum of power series; CatalanQi function; CatalanQi number; beta function
Online: 7 April 2017 (04:27:13 CEST)
ARTICLE

doi:10.20944/preprints201703.0209.v2
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
identity; inverse matrix; explicit formula; generating function; Chebyshev polynomials of the second kind; Catalan number; triangular matrix; classical hypergeometric function; integral representation
Online: 7 August 2017 (15:49:11 CEST)
ARTICLE

doi:10.20944/preprints201703.0200.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
explicit formula; recursive formula; generalized Motzkin number; Motzkin number; restricted hexagonal number; Catalan number; generating function
Online: 27 March 2017 (11:02:41 CEST)
ARTICLE

doi:10.20944/preprints201708.0004.v1
Subject:
Computer Science And Mathematics,
Computational Mathematics
Keywords:
identity; generating function; Eulerian polynomial; higher order Eulerian polynomial; Stirling number; open problem
Online: 2 August 2017 (17:03:00 CEST)
ARTICLE

doi:10.20944/preprints201708.0044.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
identity; Bell polynomial; unnamed polynomial; explicit formula; inversion theorem; Stirling number; binomial coeﬃcient
Online: 11 August 2017 (13:51:05 CEST)
ARTICLE

doi:10.20944/preprints201708.0026.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
simplification; coefficient; ordinary differential equation; higher order Bernoulli number of the second kind; Stirling number of the first kind; Stirling number of the second kind; inversion formula; Bell polynomial of the second kind; Faà di Bruno formula.
Online: 8 August 2017 (07:59:57 CEST)
ARTICLE

doi:10.20944/preprints201708.0017.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
simplification; coefficient; ordinary differential equation; higher order Frobenius–Euler number; Fa`a di Bruno formula; Bell polynomial of the second kind; inversion formula
Online: 4 August 2017 (15:47:44 CEST)
ARTICLE

doi:10.20944/preprints201704.0026.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
simple form; explicit form; differential equation; Lerch transcendent; logarithmic function
Online: 4 April 2017 (16:53:18 CEST)
ARTICLE

doi:10.20944/preprints201703.0208.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
closed expression; Fibonacci number; Fibonacci polynomial; tridiagonal determinant; Hessenberg determinant
Online: 28 March 2017 (03:11:06 CEST)
ARTICLE

doi:10.20944/preprints201703.0192.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
nonlinear ordinary differential equation; Stirling number of the first kind; simplifying; technique; combinatorial analysis
Online: 24 March 2017 (18:30:21 CET)
ARTICLE

doi:10.20944/preprints201708.0090.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
Bell number; Bell polynomial; generalization; explicit formula; inversion formula; inversion theorem; Stirling number; Bell polynomial of the second kind; determinantal inequality; product inequality; completely monotonic function; logarithmic convexity
Online: 26 August 2017 (09:12:05 CEST)
ARTICLE

doi:10.20944/preprints201703.0119.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
Lévy–Khintchine representation; integral representation; Bernstein function; Stieltjes function; Toader–Qi mean; weighted geometric mean; Bessel function of the first kind; probabilistic interpretation; probabilistic interpretation; application in engineering; inequality
Online: 16 March 2017 (11:31:31 CET)
ARTICLE

doi:10.20944/preprints201610.0043.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
viewpoint; ordinary differential equation; solution; derivative polynomial; identity; Stirling numbers; Bernoulli number; Bernoulli polynomial; FrobeniusEuler polynomial
Online: 12 October 2016 (11:47:48 CEST)
SHORT NOTE

doi:10.20944/preprints201610.0034.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
determinantal expression; recurrence relation; Euler polynomial; Euler number; Hessenberg determinant
Online: 11 October 2016 (10:40:02 CEST)
SHORT NOTE

doi:10.20944/preprints201703.0055.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
closed form; Stirling polynomial; Stirling number; Bernoulli number; Faá di Bruno's formula; Bell polynomial
Online: 10 March 2017 (10:28:19 CET)
ARTICLE

doi:10.20944/preprints201611.0146.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
explicit form; inhomogeneous linear ordinary differential equation; derivative; Lerch transcendent; absolute monotonicity; complete monotonicity; Bernstein function; inequality; diagonal recurrence relation; Stirling numbers of the first kind; logarithmic function
Online: 29 November 2016 (08:00:53 CET)
ARTICLE

doi:10.20944/preprints201611.0145.v1
Subject:
Computer Science And Mathematics,
Analysis
Keywords:
Hermite polynomial; square; generating function; higher order derivative; differential equation; derivative polynomial; explicit formula; recurrence relation
Online: 29 November 2016 (06:50:11 CET)
ARTICLE

doi:10.20944/preprints201610.0035.v1
Subject:
Computer Science And Mathematics,
Algebra And Number Theory
Keywords:
derangement number; closed form; Hessenberg determinant; tridiagonal determinant; generating function; recurrence relation; derivative
Online: 11 October 2016 (10:53:07 CEST)