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A Treatise on Linear Differential Equations - Primary Source Edition
No preview available - 2013
adjoint admits algebraic arbitrary constants belonging characteristic equation characteristic function circle consequently constant coefficients contain continuous function convergent critical point degree denote dependent variable derivatives determine different from zero differential quantic distinct functions doubly-periodic function equa equal equation of order exponent finite number follows formula func function-group fundamental integrals fundamental system given equation gives hypergeometric series hypothesis identity independent integrals indicial equation indicial function integral function integrals regular last equation linear differential equation linear functions linearly independent logarithmic derivative logarithms multiplied negative powers normal form obtained obviously orders of multiplicity path plane poles polynomial preceding prime factors quantities rational reduces region regular integrals replace respectively result roots round satisfied spherical harmonics substitution Suppose system of fundamental theorem tion transformation uniform functions unity values vanish write