Question

For a negative integer n, the factorial n!

Answer 1

Answer:

factorial is defined only for non-negative integer numbers . Factorial can be interpolated using Gamma function, hence we can have factorial of a negative number except for negative integers because gamma function is not defined at negative integers.

Answer 2

The factorials of real negative numbers, according to the current notion, are complex numbers.

• Real negative integer factorials have an imaginary portion equal to zero and are hence real numbers.
• They are presently interpolated with the usage of Euler's gamma characteristic.
• The conceptual part of factorials has been broadened on this observe to consist of actual and imaginary numbers, in addition to multifactorial.
• For the factorials of real, negative, and imaginary numbers, new capabilities primarily based totally on Euler's factorial characteristics were developed.
• Similarly, imaginary wide variety factorials are complex numbers.
• The modulus of the complicated factorials of real negative numbers and imaginary numbers are equal to the moduli of the complicated factorials of real positive numbers.
• The cautioned technique has additionally been prolonged to Euler's gamma characteristic for real negative numbers, imaginary numbers, and real negative numbers, in addition to the beta characteristic.