vurcampaign.blogg.se

Fractional factorials and multifactorials have been defined in a new perspective.

The moduli of the complex factorials of real negative numbers, and imaginary numbers are equal to their respective real positive number factorials. Similarly, the factorials of imaginary numbers are complex numbers. The factorials of real negative integers have their imaginary part equal to zero, thus are real numbers. As per the present concept, the factorials of real negative numbers, are complex numbers. New functions based on Euler’s factorial function have been proposed for the factorials of real negative and imaginary numbers. In the present paper, the concept of factorials has been generalised as applicable to real and imaginary numbers, and multifactorials. Presently, factorials of real negative numbers and imaginary numbers, except for zero and negative integers are interpolated using the Euler’s gamma function.