Methods of Mathematical Physics

absolutely convergent analytic function apply approximation asymptotic asymptotic expansion axes axis boundary bounded bounded variation circle circle of convergence coefficients components condition consider constant continuous continuous function convergent series coordinates corresponding cosh curve defined definition denote derivatives differential equation displacement equal essential singularity expansion expressed factor finite number formula Fourier Fourier series give given harmonic Hence infinite infinity integer integral interpolation interval Laplace's equation limit matrix method modulus motion multiple negative notation particle path plane poles polynomial positive potential power series range real numbers region Riemann integral rotation satisfied scalar sin² single-valued singularity sinh solution sphere surface tend to zero tensor theorem transformation uniformly convergent values vanish variable variation vector velocity waves x₁ y₁ µ² Σπί аф дх