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Learn the binomial theorem for positive integral indices with the number of examples provided here. Visit BYJU'S to get the properties and learn it in an easy and a better way
In this way, a new computational approach to the generalization of the binomial theorem is introduced. Numerous combinatorial identities are obtained from these matrix relations.doi:10.1007/s11253-013-0752-3StanimiroviS.Ukrainian Mathematical Journal...
We can also state the general format of the binomial theorem, which is called the multinomial theorem: (x1+x2+⋯+xr)n=∑n1+n2+⋯+nr=n(nn1,n2,…,nr)xn11xn22...xnrr(2.2)(x1+x2+⋯+xr)n=∑n1+n2+⋯+nr=n(nn1,n2,…,nr)x1n1x2n2...xrnr(2.2) ...
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Evaluation of the generalized Goodwin-Staton integral using binomial expansion theorem. J. Quant. Spect. Rad. Transfer., 105:8-11, 2007.B. A. Mamedov. Evaluation of the generalized Goodwin-Staton integral using binomial expansion theorem. Journal of Quantitative Spectroscopy and Radiative Transfer, ...
M. Chamberland, K. Dilcher, A binomial sum related to Wolstenholme's theorem, J. Number Theory 129 (2009), no. 11, 2659-2672.M. Chamberland, K. Dilcher, A binomial sum related to Wolstenholme's theorem, J. Number Theory 129 (11) (2009) 2659- 2672, doi:10.1016/j.jnt.2009.05.010...
Theorem 1.1. For random algebraic polynomial Pn(x), let n be separated into two multi- pliers such that n = k · m, where k = f (n) is an integer and increasing function of n, such that f (n) = O(log n)2. The random variables aj, j = 0, 1, 2, . . . , n 1 are...
(11) The above equation is non-linear, and we can solve it numerically. 3.2. Moments In this subsection, we will look at the 𝑟𝑡ℎ moment of the 𝐵𝐵𝐸2 distribution. Theorem 1. If X has an RV𝐵𝐵𝐸2(𝜆,𝜃,𝑎,𝑏)then the𝑟𝑡ℎmoment of X is provided...
(11) The above equation is non-linear, and we can solve it numerically. 3.2. Moments In this subsection, we will look at the r t h moment of the B B E 2 distribution. Theorem 1. If X has an RV B B E 2 ( λ , θ , a , b ) then the r t h moment of X is provided...