Xksuae
X k≥0 ak 1 ···a k m bk 1 ···bk n zk k!.
Xksuae. Sum of powers nX−1 k=0 km = 1 m +1 Xm k=0 m +1 k!. If the exponent r is even, then the inequality is valid for all real numbers x.The strict version of the inequality reads. In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1 + x.It is often employed in real analysis.
The inequality states that (+) ≥ +for every integer r ≥ 0 and every real number x ≥ −1. Bkn m+1−k integer n ≥ 1 Thus nX−1 k=0 km = nm+1 m +1 + lower order terms Formulas relating factorial powers and ordinary powers Stirling numbers of xn = X k (n k) xk integer n ≥ 0 the second kind Stirling numbers of xn = X k " n k # xk.
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