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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 {} denotes the fractional part of () is a Bernoulli polynomial.
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.
1.1 Mathematics. 1.2 Physics. 1.3 Chemistry. 1.4 Biology. ... This is a list of equations, ... Kirchhoff's diffraction formula;
Then the sum of the resulting series, i.e., the limit of the sequence of partial sums of the resulting series, satisfies +, = (, +,) =, +,, when the limits exist. Therefore, first, the series resulting from addition is summable if the series added were summable, and, second, the sum of the resulting series is the addition of the sums of the ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Abelian and Tauberian theorems (mathematical analysis) Absolute convergence theorem (mathematical series) Cesàro's theorem (real analysis) Hardy–Littlewood tauberian theorem (mathematical analysis) Riemann series theorem (mathematical series) Silverman–Toeplitz theorem (mathematical analysis) Śleszyński–Pringsheim theorem (continued ...
A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.
In general, any infinite series is the limit of its partial sums. For example, an analytic function is the limit of its Taylor series, within its radius of convergence. = =. This is known as the harmonic series. [6]