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... values at negative integers are given by the poly-Bernoulli numbers Bn ([9, 6]). The series (1.1) satisfies several identities. Theorem 3.1. The following identities hold where defined. i. We have Sj,r (s, a) = Sj,r (s, a + 1) + Sj,r−1 (s,Pa). ii. For r ∈ Z+ we have Sj,r (s, a) = Sj,0P (s, a) + rt ...
... values at negative integers are given by the poly-Bernoulli numbers Bn ([9, 6]). The series (1.1) satisfies several identities. Theorem 3.1. The following identities hold where defined. i. We have Sj,r (s, a) = Sj,r (s, a + 1) + Sj,r−1 (s,Pa). ii. For r ∈ Z+ we have Sj,r (s, a) = Sj,0P (s, a) + rt ...
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... In the latter case, the two copies of _3- are glued together so that we get a planar diagram symmetric on its vertical axis (see Fig. 4). This representation theorem provides a procedure to calculate \M{k)~ \, the number of elements of M(k) , from the number of elements in 3_-. But ...
... In the latter case, the two copies of _3- are glued together so that we get a planar diagram symmetric on its vertical axis (see Fig. 4). This representation theorem provides a procedure to calculate \M{k)~ \, the number of elements of M(k) , from the number of elements in 3_-. But ...
A New Connection Between the Triangles of Stirling and Pascal
... But the sequence of the number of elements in each white triangle began with 1 and this isn’t a perfect number! That’s true, Pascal’s triangle doesn’t always yield perfect numbers in this manner, but every even perfect number does appear somewhere in this sequence. This is because the number of elem ...
... But the sequence of the number of elements in each white triangle began with 1 and this isn’t a perfect number! That’s true, Pascal’s triangle doesn’t always yield perfect numbers in this manner, but every even perfect number does appear somewhere in this sequence. This is because the number of elem ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.