Results 1 to 10 of about 24,513 (140)
Finite Sums Involving Reciprocals of the Binomial and Central Binomial Coefficients and Harmonic Numbers [PDF]
Symmetry, 2021 We prove some finite sum identities involving reciprocals of the binomial and central binomial coefficients, as well as harmonic, Fibonacci and Lucas numbers, some of which recover previously known results, while the others are new.
Anthony Sofo +2 more
exaly +3 more sources
The Series of Reciprocals of Non-central Binomial Coefficients
American Journal of Computational Mathematics, 2013 Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients.
Laiping Zhang, Wanhui Ji
exaly +3 more sources
More congruences for central binomial coefficients
Journal of Number Theory, 2010 Let \(p>5\) be a prime number. The author proves that \[ \sum_{k=1}^{p-1}\frac{1}{k^2}\binom{2k}{k}^{-1}\equiv\frac13 \frac{H(1)}{p}\pmod {p^3} \] and that \[ \sum_{k=1}^{p-1}\frac{(-1)^k}{k^3}\binom{2k}{k}^{-1}\equiv-\frac25 \frac{H(1)}{p^2}\pmod {p^3}, \] where \(H(1)=\sum_{k=1}^{p-1}\frac{1}{k}\).
Roberto Tauraso
exaly +4 more sources
Spatiotemporal Trends and Co-Resistance Patterns of Multidrug-Resistant Enteric Escherichia coli O157 Infections in Humans in the United States [PDF]
PathogensMultidrug-resistant (MDR) Shiga toxin-producing Escherichia coli O157 (STEC O157) is a public health threat. This study analyzed publicly available surveillance data collected by the National Antimicrobial Resistance Monitoring System (NARMS) to assess ...
Tarjani Bhatt, Csaba Varga
doaj +2 more sources
On a divisor of the central binomial coefficient [PDF]
The Ramanujan Journal, 2021 It is well known that for all $n\geq1$ the number $n+ 1$ is a divisor of the central binomial coefficient ${2n\choose n}$. Since the $n$th central binomial coefficient equals the number of lattice paths from $(0,0)$ to $(n,n)$ by unit steps north or east, a natural question is whether there is a way to partition these paths into sets of $n+ 1$ paths or
Matthew Just, Maxwell Schneider
openaire +2 more sources
Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
doaj +1 more source
A note on a one-parameter family of non-symmetric number triangles [PDF]
Opuscula Mathematica, 2012 The recent growing interest in special Clifford algebra valued polynomial solutions of generalized Cauchy-Riemann systems in \((n + 1)\)-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to ...
Maria Irene Falcão, Helmuth R. Malonek
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Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
doaj +1 more source
Some Families of Apéry-Like Fibonacci and Lucas Series
Mathematics, 2021 In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed ...
Robert Frontczak +2 more
doaj +1 more source