In this note, we provide an analytical approximation to the exponential integral valid for all values of its argument. The approximation schaum’s outline series mathematical handbook of formulas and tables pdf constructed by interpolation between the exponential integral’s small and large asymptotes. The interpolation contains an unknown function, which is determined using the minimax criterion.

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The maximum error in the approximation is less than 0. Check if you have access through your login credentials or your institution. A previously developed method to determine the roots of transcendental trigonometric equations is herein extended to compute the eigenvalues of Bessel function characteristic equations of boundary value problems. The technique relies on the fact that Bessel functions can be conveniently approximated to simple asymptotic trigonometric expressions. The characteristic equation containing asymptotic approximations is solved by means of inverse trigonometry and each root is then used as the initial guess in the iterative process to determine the eigenvalues of the original Bessel function problem. D Dept, Ashland Chemical Inc.

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