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Accordingly adjoint algebraic equation algebraic functions arbitrary constants assigned associated coefficients consider converges degree denote derivatives determinant doubly-periodic function elementary divisors equal equation of order essential singularity exist exponents expression factor finite free from logarithms Fuchsian type fundamental equation fundamental system given Hence holomorphic function homogeneous linear relation indices indicial equation indicial function infinite initial values integral belonging integrale integrals are regular large values limited number linear differential equation linear equation linearly independent integrals multiple root negative normal integral obtained ordinary point original equation path plane pole polynomial positive integer preceding quantities rational function regular integral repeated root result right-hand side second order Shew Similarly simple root substitution synectic integral ternary form theorem transformation uniform function unity vaniah vanish vicinity zero
Page 441 - J o |_v and therefore, as w = 27r2 for n = 4, which is precisely right. 20. Transcendental functions of one variable which have no essential singularity in the finite part of the plane of the variable may be distinguished into two classes according as, to speak first of all somewhat roughly, their zeros become indefinitely dense or not, as we pass to the infinite part of the plane. If circles be described in all possible ways, each to contain a certain definite number, say N, of...