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Question
Dear Prof Randy

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
If you use the definition of a factorial as a gamma function, then non-integer real and complex numbers can be represented. Note that the factorial n! arises from integrating the gamma function by parts, which gives a repeating expression

Γ(n+1) = nΓ(n).

If you could find such a repeating representation using a trigonometric function, then I guess you could consider it a factorial representation.

Good luck!

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography

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