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Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
The complete graph K 4 has ten matchings, corresponding to the value T(4) = 10 of the fourth telephone number. In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls.
The Erlang distribution is the distribution of a sum of independent exponential variables with mean / each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of . The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the events that occur in a ...
The sum is taken over all combinations of nonnegative integer indices k 1 through k m such that the sum of all k i is n. That is, for each term in the expansion, the exponents of the x i must add up to n. [2] [a] In the case m = 2, this statement reduces to that of the binomial theorem. [2]
In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers.
Fermat's Last Theorem states that for powers greater than 2, the equation a k + b k = c k has no solutions in non-zero integers a, b, c. Extending the number of terms on either or both sides, and allowing for higher powers than 2, led to Leonhard Euler to propose in 1769 that for all integers n and k greater than 1, if the sum of n k th powers ...
The sum is a sum over all partitions of p. Another exact nested sum expansion for these Stirling numbers is computed by elementary symmetric polynomials corresponding to the coefficients in x {\displaystyle x} of a product of the form ( 1 + c 1 x ) ⋯ ( 1 + c n − 1 x ) {\displaystyle (1+c_{1}x)\cdots (1+c_{n-1}x)} .