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Geometry/Computing Factorial of a Number

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Question
Dear Prof Azeem

http://en.wikipedia.org/wiki/Factorial
http://en.wikipedia.org/wiki/Mathematical_constant

Is it possible to compute the factorial for the following ?.

1. Surd
2. Complex number
3. Decimal number
4. trigonometric function sin, tan, cosec etc
5. mathematical constant

Can factorial inverse of a number can be defined with a new mathematical symbol ?.

Awaiting our reply,

Thanks & Regards,
Prashant S Akerkar

Answer
Hi Prashant,

There gamma function will be of interest to you.  It is a function that agrees with the factorial on the positive integers, but is also defined over the reals and the complex numbers.

For the factorial inverse, one could use the inverse of the gamma function, using the superscript -1 to denote inverse.

Best regards,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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