(vol. V-VI) Partial differential equations. 1906At the University Press, 1902 - Differential equations |
Common terms and phrases
a₁ Accordingly algebraic equation algebraic functions associated B₁ c₁ c₂ characteristic index coefficients consider converges Crelle degree denote derivatives determinant dm-w domain doubly-periodic function elementary divisors equal equation of order essential singularity exponents expression factor finite free from logarithms Fuchsian type fundamental equation fundamental system given Hence holomorphic function indicial equation indicial function infinite initial values integral belonging integrals are regular k₁ large values limited number linear combination linear differential equation linear equation linearly independent integrals minors multiple root normal integral obtained ordinary point original equation P₁ plane polynomial positive integer powers preceding quantities rational function regular integrals result right-hand side second order Shew simple root sub-group substitution synectic integral theorem u₁ uniform functions unity v₁ vanish variable vicinity of x=0 w₁ y₁ zero
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Page 429 - 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...