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Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

By analogy with the sinc function, define the sinhc function by sinhc(z)={(sinhz)/z for z!=0; 1 for z=0. (1) Since sinhx/x is not a cardinal function, the "analogy" with the ...

By analogy with the tanc function, define the tanhc function by tanhc(z)={(tanhz)/z for z!=0; 1 for z=0. (1) It has derivative (dtanhc(z))/(dz)=(sech^2z)/z-(tanhz)/(z^2). (2) ...

An apodization function A(x)=1, (1) having instrument function I(k)=2asinc(2pika). (2) The peak of I(k) is 2a. The full width at half maximum of I(k) can found by setting ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

The apodization function A(x)=1-(x^2)/(a^2). (1) Its full width at half maximum is sqrt(2)a. Its instrument function is I(k) = 2asqrt(2pi)(J_(3/2)(2pika))/((2pika)^(3/2)) (2) ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...