New Characterizations for the Eigenvalues of the Prolate Spheroidal Wave Equation

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• 作者：F. Richard-Jung ; J.-P. Ramis ; J. Thomann and F. Fauvet
• 刊名：Studies in Applied Mathematics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：138
• 期：1
• 页码：3-42
• 全文大小：370K
• ISSN：1467-9590

文摘

In this paper, we give new characterizations for the eigenvalues of the prolate wave equation as limits of the zeros of some families of polynomials: the coefficients of the formal power series appearing in the solutions near 0, 1, or ∞ (in the variables equation-construct="true" class="math-equation-construct">equation-image="true" class="math-equation-image">equation-mathml="true" class="math-equation-mathml" style="display:none">x,x−1, or equation-construct="true" class="math-equation-construct">equation-image="true" class="math-equation-image">equation-mathml="true" class="math-equation-mathml" style="display:none">1/x, respectively). The result, which seems to be true for all values of the parameter τ, according to our numerical experiments, is here proved for small values of the parameter τ.