Search results
Results from the WOW.Com Content Network
A series may also be represented with capital-sigma notation: [8] [16] ... for instance an arithmetic series has partial sums = ...
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
The product above is a reflection of the fundamental theorem of arithmetic. Euler noted that if there were only a finite number of primes, then the product on the right would clearly converge, contradicting the divergence of the harmonic series.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
In capital-sigma notation this is expressed = or = + with a n > 0 for all n. Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit .
Divisor function σ 0 (n) up to n = 250 Sigma function σ 1 (n) up to n = 250 Sum of the squares of divisors, σ 2 (n), up to n = 250 Sum of cubes of divisors, σ 3 (n) up to n = 250. In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.
In zeta function regularization, the series = is replaced by the series =. The latter series is an example of a Dirichlet series. When the real part of s is greater than 1, the Dirichlet series converges, and its sum is the Riemann zeta function ζ(s).