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The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

Let A(n) denote the number of partitions of n into parts =2,5,11 (mod 12), let B(n) denote the number of partitions of n into distinct parts =2,4,5 (mod 6), and let C(n) ...

The hyperbolic cosine is defined as coshz=1/2(e^z+e^(-z)). (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

The modified bessel function of the second kind is the function K_n(x) which is one of the solutions to the modified Bessel differential equation. The modified Bessel ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...