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A 
mathematical expression expressed using a finite number of basic arithmetic operations over the numbers, elementary functions or tabulated special functions and may include infinite series and continued fractions.


the key difference with Closed-form expression is that 

The key benefit of dealing with closed-form expressions is that they are analytic expression may include tabulated special functions and may include infinite series and continued fractions.


  • well tabulated with precision enough for the majority of engineering applications
  • implemented as fast-computable algorithms with computer precisions (usually 64 bit and 128 bit) on modern  computers
  • available as fast-computing algorithms with arbitrary user-defined precision

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