Bounds for Jaeger integrals

详细信息    查看全文

• 作者：árpád Baricz ; Tibor K. Pogány ; Saminathan Ponnusamy…
• 关键词：Jaeger function ; Lower incomplete Gamma function ; Upper incomplete Gamma function ; Bessel functions of the first and second kind ; Modified Bessel function of the second kind ; Primary 26D15 ; Secondary 33B20 ; 33C10
• 刊名：Journal of Mathematical Chemistry
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：53
• 期：5
• 页码：1257-1273
• 全文大小：228 KB
• 参考文献：1. Jaeger, JC (1942) Proc. R. Soc. Edinb. A 61: pp. 223 r> 2. Phillips, WRC, Mahon, PJ (2011) Proc. R. Soc. A 467: pp. 3570 rnal" href="http://dx.doi.org/10.1098/rspa.2011.0301" target="_blank" title="It opens in new window">CrossRef r> 3. Baricz, á, Pogány, TK (2013) Acta Polytech. Hung. 10: pp. 53 r> 4. Baricz, á, Pogány, TK (2014) Math. Inequal. Appl. 17: pp. 989 r> 5. Smith, LP (1937) J. Appl. Phys. 8: pp. 441 rnal" href="http://dx.doi.org/10.1063/1.1710319" target="_blank" title="It opens in new window">CrossRef r> 6. Jaeger, JC (1941) Proc. R. Soc. Edinb. A 61: pp. 223 r> 7. Carlslaw, HS, Jaeger, JC (1959) Conduction of Heat in Solids. Oxford University Press, Oxford r> 8. Nicholson, JW (1921) Proc. R. Soc. Lond. A 100: pp. 226 rnal" href="http://dx.doi.org/10.1098/rspa.1921.0083" target="_blank" title="It opens in new window">CrossRef r> 9. Chessin, AS (1902) Comptes Rendus 135: pp. 678 r> 10. Chessin, AS (1903) Comptes Rendus 136: pp. 1124 r> 11. Baricz, á, Jankov, D, Pogány, TK (2012) Integr. Transf. Spec. Funct. 23: pp. 529 rnal" href="http://dx.doi.org/10.1080/10652469.2011.609483" target="_blank" title="It opens in new window">CrossRef r> 12. Grosswald, E (1976) Ann. Probab. 4: pp. 680 rnal" href="http://dx.doi.org/10.1214/aop/1176996038" target="_blank" title="It opens in new window">CrossRef r> 13. Ismail, MEH (1977) Ann. Probab. 5: pp. 582 rnal" href="http://dx.doi.org/10.1214/aop/1176995766" target="_blank" title="It opens in new window">CrossRef r> 14. Hamana, Y (2012) Osaka J. Math. 49: pp. 853 r> 15. Y. Hamana, H. Matsumoto, T. Shirai, ref="http://arxiv.org/abs/1302.5154v1" class="a-plus-plus">arXiv:1302.5154v1 (2013) r> 16. E.C.J. von Lommel, Abh. der math. phys. Classe der k. b. Akad. der Wiss. (München) 15 529 (1884-886) r> 17. Watson, GN (1922) A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge r> 18. Minakshisundaram, S, Szász, O (1947) Trans. Am. Math. Soc. 61: pp. 36 rnal" href="http://dx.doi.org/10.1090/S0002-9947-1947-0019148-1" target="_blank" title="It opens in new window">CrossRef r> 19. L. Landau, in / Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory, ed. by H. Warchall (Berkeley, CA: June 11-3, 1999), 147 (2000); Electronic J. Differential Equations 4 (2002), Southwest Texas State University, San Marcos, TX r> 20. Krasikov, I (2006) J. Appl. Anal. 12: pp. 83 rnal" href="http://dx.doi.org/10.1515/JAA.2006.83" target="_blank" title="It opens in new window">CrossRef r> 21. Olenko, AY (2006) Integral Transforms Spec. Funct. 17: pp. 455 rnal" href="http://dx.doi.org/10.1080/10652460600643445" target="_blank" title="It opens in new window">CrossRef r> 22. Ifantis, EK, Siafarikas, PD (1990) J. Math. Anal. Appl. 147: pp. 214 rnal" href="http://dx.doi.org/10.1016/0022-247X(90)90394-U" target="_blank" title="It opens in new window">CrossRef r> 23. á. Baricz, P.L. Butzer, T.K. Pogány, in / Analytic Number Theory, Approximation Theory, and Special Functions—In Honor of Hari M. Srivastava, vol. 775, ed. by T. Rassias, G. V. Milovanovi? (Springer, New York, 2014) r> 24. Cerone, P In: rs">Cerone, P, Dragomir, S eds. (2008) Advances in Inequalities for Special Functions. Nova Science Publishers, New York r> 25. Srivastava, HM, Pogány, TK (2007) Russian J. Math. Phys. 14: pp. 194 rnal" href="http://dx.doi.org/10.1134/S1061920807020082" target="_blank" title="It opens in new window">CrossRef r> 26. Baricz, á, Jankov, D, Pogány, TK (2012) Proc. Am. Math. Soc. 140: pp. 951 rnal" href="http://dx.doi.org/10.1090/S0002-9939-2011-11402-3" target="_blank" title="It opens in new window">CrossRef r> rs">Olver, FWJ, Lozier, DW, Boisvert, RF, Clark, CW eds. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge r> 27. Alzer, H (1997) Math. Comput. 66: pp. 771 rnal" href="http://dx.doi.org/10.1090/S0025-5718-97-00814-4" target="_blank" title="It opens in new window">CrossRef r> 28. Gautschi, W (1959) J. Math. Phys. 38: pp. 77 r>
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistryr>Physical Chemistryr>Theoretical and Computational Chemistryr>Mathematical Applications in Chemistryr>
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

Lower and upper bounds are deduced for some Jaeger integrals which involve the Bessel functions of the first and second kind. The upper bounds contain some elementary functions as well as incomplete gamma functions, while the lower bounds are expressed also in terms of incomplete gamma functions and are deduced via some known inequalities for Bessel functions of the first and second kinds.