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Mathematical tables are lists of numbers showing the results of a calculation with varying arguments.Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation.
The idea of the proof of the class number formula is most easily seen when K = Q(i).In this case, the ring of integers in K is the Gaussian integers.. An elementary manipulation shows that the residue of the Dedekind zeta function at s = 1 is the average of the coefficients of the Dirichlet series representation of the Dedekind zeta function.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
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.
This formula follows from the multiplicative formula above by multiplying numerator and denominator by (n − k)!; as a consequence it involves many factors common to numerator and denominator. It is less practical for explicit computation (in the case that k is small and n is large) unless common factors are first cancelled (in particular ...
By taking conjugates, the number p k (n) of partitions of n into exactly k parts is equal to the number of partitions of n in which the largest part has size k. The function p k (n) satisfies the recurrence p k (n) = p k (n − k) + p k−1 (n − 1) with initial values p 0 (0) = 1 and p k (n) = 0 if n ≤ 0 or k ≤ 0 and n and k are not both ...
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