coshxy

Coshxy is a mathematical function that represents the hyperbolic cosine of the product of two variables, x and y. It is defined as cosh(xy), where cosh is the hyperbolic cosine function. The hyperbolic cosine function is one of the hyperbolic functions, which are analogs of the trigonometric functions but based on the hyperbola rather than the circle.

The hyperbolic cosine function is defined as cosh(z) = (e^z + e^(-z)) / 2, where e is the base of the natural logarithm and z is a complex number. When applied to the product of two variables, coshxy becomes (e^(xy) + e^(-xy)) / 2.

Coshxy is used in various fields of mathematics and physics, including complex analysis, differential equations, and special functions. It is particularly useful in contexts where the product of variables is involved, such as in certain types of differential equations or when dealing with products of complex numbers.

The function coshxy shares some properties with the ordinary hyperbolic cosine function. For example, it is an even function, meaning coshxy = cosh(-xy). It is also periodic with a period of 2πi, meaning coshxy = cosh(xy + 2πik) for any integer k. Additionally, coshxy is always greater than or equal to 1 for all real values of x and y.

In summary, coshxy is a mathematical function that represents the hyperbolic cosine of the product of two variables. It is defined as (e^(xy) + e^(-xy)) / 2 and shares many properties with the ordinary hyperbolic cosine function. It is used in various fields of mathematics and physics, particularly in contexts involving the product of variables.