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Glasser Function


GlasserFunction

The interesting function defined by the definite integral

 G(x)=int_0^xsin(tsint)dt,

illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a number of remarkable properties, the foremost of which is that the first "hump" has a single subhump, the second hump has two subhumps, and so on. The function is asymptotic to

 G(x)∼2sqrt(x/pi).
GlasserFunctionDerivatives

The derivatives of the Glasser function are illustrated above.


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References

Glasser, M. L. and Cosgrove, C. "Problem 785." Nieuw Arch. Wisk. 8, 455, 1990.

Referenced on Wolfram|Alpha

Glasser Function

Cite this as:

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

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