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 Sep24 awarded Autobiographer Aug23 comment Simplify $\tan^{-1}[(\cos x - \sin x)/(\cos x + \sin x)]$ define simplest please. Jul23 awarded Supporter Jul3 awarded Teacher Jun13 revised Compound Poisson process with exponential distribution added 12 characters in body Jun13 awarded Editor Jun13 revised Compound Poisson process with exponential distribution added 10 characters in body Jun13 answered Compound Poisson process with exponential distribution Jul21 revised Method for variable substitution in multiple summation added a tag Jul21 comment Method for variable substitution in multiple summation Yes they are:( I used one of the explicit sum formulas of Chebyshev polynomial (mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html eq.15), which introduces those floor functions. Jul21 comment Method for variable substitution in multiple summation @ Christian Blatter: Thanks very much for your answer. I understand the difficulties of counting lattice points in disk, but if considering the summation region bounded only by integer coefficients planes (like $\sum_k A_k x_k=B$ where $A_k, B\in \mathbb{Z}$), the problem might be much simpler and there might even exist a systematical technique for it. Besides, I'm thinking of using Iverson's bracket to avoid dealing with those tricky boundary conditions. Jul21 comment Method for variable substitution in multiple summation @Patrick Da Silva: Yes I draw 2-dim or 3-dim axes too when I do the transformation by hand :D But if I have many levels of sum, this will be inefficient cause it's hard to draw high dimension, and those floor and ceiling functions and steps$\neq 1$ are bothering. I think I need to treat the whole summation region as a high dimension polyhedron and find a systematical routine to deal with it. Jul21 awarded Student Jul21 asked Method for variable substitution in multiple summation