The Sharper Form of Brunn-Minkowski Type Inequality for Boxes

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Tınaztepe G., Kemali S., Sezer S., Eken Z.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.50, sa.2, ss.377-386, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.xx
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.377-386
  • Anahtar Kelimeler: confluent hypergeometric function, convolution theorem, error function, Gaussian hypergeometric function, generalized hypergeometric function, Laplace transform, parabolic cylinder function
  • Akdeniz Üniversitesi Adresli: Evet

Özet

This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently specialized for products of the error function and its complement thereby yielding new integral representations for products of the latter two functions. The transforms that are derived in this paper also allow to correct two inverse Laplace transforms that are widely reported in the literature and subsequently uses one of the corrected expressions to obtain two new definite integrals for the generalized hypergeometric function.