Pseudogamma function

The pseudogamma function is a mathematical function that generalizes the concept of the gamma function. While the traditional gamma function, denoted as \(\Gamma(z)\), is defined for complex numbers with a positive real part, the pseudogamma function can be used in a wider context, particularly in the field of number theory and special functions. One common interpretation of the pseudogamma function is based on the notion of providing alternatives or approximations to the gamma function.