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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 3

On the Logarithmic Integral

Brian FİSHER
Biljana Jolevska TUNESKA
Sayfa
393–401
Yayın Tarihi
2022-10-18
DOI
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Some convolutions and neutrix convolutions of these functions and other functions are then found.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The logarithmic integral li(x) and its associated functions li+(x) and li−(x) are defined as locally summable functions on the real line.
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Temel Bulgular & Veri:The logarithmic integral li(x) and its associated functions li+(x) and li−(x) are defined as locally summable functions on the real line.
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Sonuç & Katkı:Some convolutions and neutrix convolutions of these functions and other functions are then found.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Logarithmic integral · Distribution · Convolution

Abstract

The logarithmic integral li(x) and its associated functions li+(x) and li−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of these functions and other functions are then found.

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Bu Makaleye Atıf Yap

FİSHER, B., TUNESKA, B. J. (2022). On the Logarithmic Integral. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 3, 393–401. https://ajindex.com/articles/530637

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Kaynakça (5)

  1. Abramowitz, M. and Stegun, I. A. (Eds). Handbook of Mathematical Functions with Formu- las, Graphs and Mathematical Tables, 9th printing(New York: Dover, p. 879, 1972). van der Corput, J. G. Introduction to the neutrix calculus, J. Analyse Math. 7, 291–398, 1959-60.
  2. Fisher, B. Neutrices and the convolution of distributions, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 17, 119–135, 1987.
  3. Fisher, B., Jolevska-Tuneska, B. and Taka˘ci, A. On convolutions and neutrix convolutions involving the incomplete gamma function, Integral Transforms and Special Functions 15 (5), 404–415, 2004.
  4. Jolevska-Tuneska, B. and Taka˘ci, A. Results on the commutative neutrix convolution product of distributions, Hacettepe J. Math. Stat. 37 (2), 135–141, 2008. Gel’fand, I. M. and Shilov, G. E. Generalized functions, Vol. I (Academic Press Chap. 1, 1964).
  5. Jones, D. S. The convolution of generalized functions, Quart. J. Math. Oxford 24 (2), 145– 163, 1973.