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Risk factors for highly pathogenic avian influenza outbreaks in Japan during 2022-2023 season identified by additive Bayesian network modeling. [PDF]
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The generalization of the binomial theorem
Journal of Mathematical Physics, 1989As is well known, the binomial theorem is a classical mathematical relation that can be straightforwardly proved by induction or through a Taylor expansion, albeit it remains valid as long as [A,B]=0. In order to generalize such an important equation to cases where [A,B]≠0, an algebraic approach based on Cauchy’s integral theorem in conjunction with ...
J. Morales, A. Flores‐Riveros
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The Mathematics Teacher, 1960
An example shows how a teacher may enrich the students’ learning of the binomial theorem.
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An example shows how a teacher may enrich the students’ learning of the binomial theorem.
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A Proof of the Binomial Theorem
The American Mathematical Monthly, 1974(1974). A Proof of the Binomial Theorem. The American Mathematical Monthly: Vol. 81, No. 4, pp. 390-393.
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2019
You may have wondered why the numbers \(\left( {\begin{array}{c}n\\ k\end{array}}\right) \) are called binomial coefficients, and not the “choice numbers” or “combination numbers” or something related to subsets. Why “binomial”? We’ll see why in this chapter, which begins a theme for us: encoding combinatorial results algebraically.
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You may have wondered why the numbers \(\left( {\begin{array}{c}n\\ k\end{array}}\right) \) are called binomial coefficients, and not the “choice numbers” or “combination numbers” or something related to subsets. Why “binomial”? We’ll see why in this chapter, which begins a theme for us: encoding combinatorial results algebraically.
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The Story of the Binomial Theorem
The American Mathematical Monthly, 1949(1949). The Story of the Binomial Theorem. The American Mathematical Monthly: Vol. 56, No. 3, pp. 147-157.
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A Proof of the Binomial Theorem
The Mathematical Gazette, 1933In teaching algebra, it is obviously desirable to prove the Binomial Theorem for a real (or at any rate for a rational) index without assuming certain theorems on convergence which are used in Euler’s proof. So far as I know, no one has thought it worth while to devise such a proof.
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Local Theorems for the Markov Binomial Distribution
Lithuanian Mathematical Journal, 2001The Markov binomial distribution was considered by many authors [cf. \textit{R. L. Dobrushin}, Izv. Akad. Nauk SSSR, Ser. Mat. 17, 291--330 (1953; Zbl 0052.14301); \textit{J. Gani}, J. Appl. Probab., Spec. Vol. 19A, 321--326 (1982; Zbl 0488.60074); \textit{B. O. Koopman}, Proc. Natl. Acad. Sci. USA 36, 202--207 (1950; Zbl 0037.08502); \textit{R.
M. Mikalauskas, Vydas Čekanavičius
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