abstract:In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions—constants, one variable x, elementary operations of arithmetic (+ − × ÷), nth roots, exponent and logarithm (which thus also include trigonometric functions and inverse trigonometric functions).
The closed-formexpression for the mean squared beamwidthofannularbeamspropagatingthroughatmosphericturbulence is derivedby using theintegraltransformtechnique.