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Semi-Integral

A fractional integral of order 1/2. The semi-integral of t^lambda is given by

D^(-1/2)t^lambda=(t^(lambda+1/2)Gamma(lambda+1))/(Gamma(lambda+3/2)),

so the semi-integral 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+3/2))=2csqrt(t/pi).

See also

Fractional Integral, 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

Semi-Integral

Cite this as:

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

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