The Distribution of Characteristic Values of a Linear Boundary Problem of the Second Order Based on a Differential Equation with a Turning Point |
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a₁ a₁₂ A₂ American Mathematical Society Anna Chandapillai asymptotic forms asymptotic solutions axis of imaginaries axis of reals b₁ b₁₂ Bessel functions boundary conditions boundary problem defined C₁ C₂ characteristic values explicit Cochin coefficients complex plane curves D₁₂ D₂ denote derived differential equation 1.1 differential system 1.3 discussed by Langer DISTRIBUTION OF CHARACTERISTIC Doctor of Philosophy epsilon function equation in sector explicit form explicit to terms exponential sums H₁ Hence integer Langer in paper linear differential equation linearly independent Log H₂ logh means of relations mildly irregular P₁ P₂ pair of solutions polynomials H positive integer q log range regular boundary problem relations 3.8 represented asymptotically S₂ SECOND ORDER BASED sector S3 similar strip bounded Substituting this value terms containing logk terms in powers U₂ UNIVERSITY OF WISCONSIN V₂ values in sector written Wronskian वेळ るい るじ