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International Journal of Statistika And Mathematika ISSN: 2277-2790 E-ISSN: 2249-8605

Volume 2, Issue 3, 2012 pp 13-20

 

Research Article

 

On Hankel type transform of generalized Mathieu series

 

B.B.Waphare

MAEER’s MIT ACSC, Alandi, Pune-412105, Maharashtra, India

Academic Editor: Dr. Jadhav V.A.

 

References

 

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[3]   A. Erdelyi, W.  Magnus, F. Oberhettinger and F.G. Tricomi (Ed-S), Higher Transcedental Functions, Vols. 1-2-3, McGraw Hill, N. York-Toronto-London, 1953.

[4]   N. Elezovic, H.M. Srivastava, Z. Tomovski, Integral representations and integral transforms of some families of Mathieu type series. Integral Transforms and Special Functions, 19; No.7, pp. 481-495, 2008.

[5]   O. Emersleben, Uber die Reihe. Math. Ann. 125, pp. 165-171, 1952.

[6]   I.S.Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, N. York-London, 1965.

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[8]   E.L.Mathieu, Traite’ de Physique Mathematique. VI-VII : Theory de l’ Elasticite’ des Corps Solides (Part2). Gauthier Villars, Paris, 1890.

[9]   A.R. Miller and H.M. Srivastava, On the Mellin transform of a product of hypergeometric functions, J. Austral. Math. Soc. Ser. B40, pp. 222-237, 1998.

[10]                       T.K. Pogany, H.M. Srivastava, Z. Tomovski, some families of Mathieu a-series and alternating Mathieu a-series, Appl. Math. Computation 173, pp. 69-108, 2006.

[11]                       A.P. Prudnikov, Yu. A. Brychkov O.I. Marichev, Integrals and series, Vol.1: Elementary Functions; Vol.2, Special Functions Gordon and Breach Sci. Publ., N.York (1992): Russian Original Nauka, Moscow, 1981.

[12]                       A.P. Prudnikov, Yu. A. Brychkov, O.I. Marichev, Integrals and series (More Special Functions), Gordon and Breach Sci. Publ. N. York (1990): Russian Original: Nauka, Moscow, 1981.

[13]                       F. Qi, An integral expression and some inequalities of Mathieu type series, Rostock, Math. Kolloq. 58, pp. 37-46, 2004.

[14]                       H.M. Srivastava, Z. Tomovski, Some problems and solutions involving Mathieu’s series and its generalizations J. Inequal Pure Appl. Math. 5 No.2, Article 45, pp. 1-13 (electronic), 2004.

[15]                       H.M. Srivastava and H.L. Manocha, A Treatise of Generating Functions, Halsted Press (Ellis Horwood Ltd. Chichester), J. Wiley & Sons, N. York-Chichester-Brisbane-Toronto, 1984.

[16]                       Z. Tomovski ; K. Trencevski, On an open problem of Bai-Ni Guo and Feng Qi. J. Inequal. Pure Appl. Math. 4, No.2, Article 29, pp. 1-7 (electronic), 2003.

[17]                       Z. Tomovski, New double inequality for Mathieu Series, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. 15 pp. 79-83, 2004.

[18]                       Z. Tomovski, Integral representations of generalized Mathieu Series Via Mittag-Leffler type functions. Fract. Calc. and Appl. Anal. 10, No. 2, pp. 127-138, 2007.

[19]                       Z. Tomovski, New integral and series representations of the generalized Mathieu Series. Appl. Anal. Discrete Math. 2, No.2, pp. 205-212, 2008.

[20]                       Z. Tomovski, Vu Kim Taun, On Fourier transforms and summation formulas of generalized Mathieu Series. Math. Science Res. J; To appear, 2009. 

 

 

 
 
 
 
 
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