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<p>In this article, based on Ogasawara’s theorem (2021, JMVA, Theorem 1), we add results or corollaries mainly for the Gaussian untruncated cross-product absolute moments (GPAMs) of real-valued orders using infinite series, where for the untruncated GPAMs the formula has been simplified in that the sign functions used by Ogasawara’s theorem are removed in the general <i>n</i>-variate case. The cases <i>n</i> = 2 and 3 receive special attention. We also provide the Gaussian untruncated non-absolute product moments of integer orders for the <i>n</i>-variate case using finite series. Numerical illustrations of <i>n</i> = 2,…,5 with some comparisons to the values of the known algebraic formulas are shown.</p>

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Series formulas for the untruncated Gaussian product moments

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Haruhiko Ogasawara

摘要

In this article, based on Ogasawara’s theorem (2021, JMVA, Theorem 1), we add results or corollaries mainly for the Gaussian untruncated cross-product absolute moments (GPAMs) of real-valued orders using infinite series, where for the untruncated GPAMs the formula has been simplified in that the sign functions used by Ogasawara’s theorem are removed in the general n-variate case. The cases n = 2 and 3 receive special attention. We also provide the Gaussian untruncated non-absolute product moments of integer orders for the n-variate case using finite series. Numerical illustrations of n = 2,…,5 with some comparisons to the values of the known algebraic formulas are shown.