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In mathematics , the stationary phase approximation is a basic principle of asymptotic analysis , applying to oscillatory integrals. mathematics. mathematics. asymptotic analysis. asymptotic analysis. taken over n-dimensional space ℝn where i is the imaginary unit .. imaginary unit. imaginary unit. Here f and g are real-valued smooth functions .. The role of g is to ensure convergence ; that is , g is a test function .. test function. test function. The large real parameter k is considered in the limit as .. This method originates from the 19th century , and is due to George Gabriel Stokes and Lord Kelvin .. George Gabriel Stokes. George Gabriel Stokes. Lord Kelvin. Lord Kelvin