Results 111 to 120 of about 33,775 (162)
The fitness landscape of a form II rubisco in a photosynthetic bacterium guides engineering of oxygen tolerance. [PDF]
Sci AdvHoffmann UA +14 more
europepmc +1 more source
Digital infrastructure to support and share daily high-throughput experimental materials research.
Faraday DiscussMittmann LA +11 more
europepmc +1 more source
Assistive algorithms influence neural representations in motor brain-computer interfaces. [PDF]
Nat CommunRajeswaran P +3 more
europepmc +1 more source
Some of the next articles are maybe not open access.
Related searches:
Related searches:
A Combinatorial Identity and the World Series
SIAM Review, 1993In this note the author gives a simple probabilistic proof of a combinatorial identity by calculating the winning probability in the World Series. The winning probabilities and the expected length of the championship series are given by the applications of the identity and its generalization.
exaly +2 more sources
A Family of Combinatorial Identities
Canadian Mathematical Bulletin, 1972In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,1.1and obtained the following infinite family of identities:For A= 1,2, 3,…, let1.2where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then1.3As Eden noted, Fh(b;x) is the generating function of ph(m, n) which ...
Andrews, G. E. +2 more
openaire +1 more source
COMBINATORIAL IDENTITIES AND HYPERGEOMETRIC FUNCTIONS
Rocky Mountain Journal of Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Richards, Kendall C.
openaire +1 more source
On two combinatorial identities
Journal of Computational Methods in Sciences and Engineering, 2017Two combinatorial identities are proved. The first one allows easy to establish connections between Bernoulli and Stirling numbers and values of zeta function of integer arguments and to find numerous identities, including the new ones, for these quantities.
openaire +1 more source
Publicationes Mathematicae Debrecen, 2022
The author proves that the only solution of the difference equation \[ \Phi (2(v+1))+\sum^{v}_{k=1}\binom{2v}{2k-1} \Phi (2k) \Phi (2(v-k+1))=0 \] subject to the initial condition \(\Phi (2)=1/4\) is \(\Phi (2k)=((2^{2k}-1)/2k) B_{2k}\) where the \(B_{2k}\) are the even-indexed Bernoulli numbers. Using this result, he then proves that (1/k)\(| B_{2k}|^{
openaire +2 more sources
The author proves that the only solution of the difference equation \[ \Phi (2(v+1))+\sum^{v}_{k=1}\binom{2v}{2k-1} \Phi (2k) \Phi (2(v-k+1))=0 \] subject to the initial condition \(\Phi (2)=1/4\) is \(\Phi (2k)=((2^{2k}-1)/2k) B_{2k}\) where the \(B_{2k}\) are the even-indexed Bernoulli numbers. Using this result, he then proves that (1/k)\(| B_{2k}|^{
openaire +2 more sources