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Semiderivative

A fractional derivative of order 1/2. The semiderivative of t^lambda is given by

D^(1/2)t^lambda=(t^(lambda-1/2)Gamma(lambda+1))/(Gamma(lambda+1/2)),

so the semiderivative of the constant function f(t)=c is given by

D^(1/2)c=clim_(lambda->0)(t^(lambda-1/2)Gamma(lambda+1))/(Gamma(lambda+1/2))=c/(sqrt(pit)).

See also

Derivative, Fractional Derivative, Semi-Integral

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References

Spanier, J. and Oldham, K. B. An Atlas of Functions. Washington, DC: Hemisphere, pp. 8 and 14, 1987.

Referenced on Wolfram|Alpha

Semiderivative

Cite this as:

Weisstein, Eric W. "Semiderivative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Semiderivative.html

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