Scholarlink

<p>We prove an explicit formula for the <i>p</i>-adic valuation of the Legendre polynomials <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P_n(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> evaluated at a prime <i>p</i>, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the p-adic valuations of values of Legendre polynomials

  • 期刊论文

  • 发表日期：

    2026年5月11日

查看全文
  • Max A. Alekseyev,
  • Tewodros Amdeberhan,
  • Jeffrey Shallit,
  • Ingrid Vukusic

摘要

We prove an explicit formula for the p-adic valuation of the Legendre polynomials \(P_n(x)\) P n ( x ) evaluated at a prime p, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.