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Original Articles

A generalization of the Widder potential transform and applications

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Pages 391-401 | Received 02 Nov 2009, Accepted 16 Jul 2010, Published online: 21 Dec 2010

References

  • Brown , D. , Dernek , N. and Yürekli , O. 2007 . Identities for the E2, 1-transform and their applications . Appl. Math. Comput. , 187 : 1557 – 1566 .
  • Dernek , N. , Srivastava , H. M. and Yürekli , O. 2007 . Parseval–Goldstein type identities involving the ℒ4-transform and 𝒫4-transform and their applications . Integral Transforms Spec. Funct. , 18 : 245 – 253 .
  • Dernek , N. , Srivastava , H. M. and Yürekli , O. 2008 . Some Parseval–Goldstein type identities involving the -transform, the -transform and the 𝒫4-transform and their applications . Appl. Math. , 202 : 327 – 337 .
  • Erdélyi , A. , Magnus , W. , Oberhettinger , F. and Tricomi , F. G. 1954 . Tables of Integral Transforms , Vol. I , New York, Toronto and London : McGraw-Hill Book Company .
  • Glasser , M. L. 1973 . Some Bessel function integrals . Kyungpook Math. J. , 13 : 171 – 174 .
  • Goldstein , S. 1932 . Operational representations of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder function . Proc. London Math. Soc. (Ser. 2) , 34 : 103 – 125 .
  • Gradshteyn , I. S. and Ryzhik , I. M. 1980 . Table of Integrals, Series, and Products , 5 , Orlando, San Diego, New York, London, Toronto, Montreal, Sydney and Tokyo : Academic Press, Inc .
  • Hirschman , I. I. and Widder , D. V. 1955 . The Convolution Transform , Princeton, NJ : Princeton University Press .
  • Kahramaner , Y. , Srivastava , H. M. and Yürekli , O. 1995 . A theorem on the Glasser transform and its applications . Complex Var. Theory Appl. , 27 : 7 – 15 .
  • Prudnikov , A. P. , Bryckov , Yu. A. and Marichev , D. I. 1992 . Integrals and Series , Vol. 4 , New York, Reading, Paris, Montreux, Tokyo and Melbourne : Academic Press, Gordon and Breach Science Publishers .
  • Srivastava , H. M. and Singh , S. P. 1985 . A note the Widder transform related to the Poisson integral for a half plane . Int. J. Math. Ed. Sci. Tech. , 16 : 675 – 677 .
  • Srivastava , H. M. and Yürekli , O. 1995 . A theorem on a Stieltjes-type integral transform and its applications . Complex Var. Theory Appl. , 28 : 159 – 168 .
  • Widder , D. V. 1966 . A transform related to the Poisson integral for a half-plane . Duke Math. J. , 33 : 355 – 362 .
  • Yürekli , O. 1989 . A Parseval-type theorem applied to certain integral transforms . IMA J. Appl. Math. , 42 : 241 – 249 .
  • Yürekli , O. 1992 . An inversion theorem for the Widder potential transform . Int. J. Math. Ed. Sci. Tech. , 23 : 152 – 154 .
  • Yürekli , O. 1999 . Theorems on ℒ2-transforms and its applications . Complex Var. Theory Appl. , 38 : 95 – 107 .
  • Yürekli , O. 1999 . New identities involving the Laplace and the ℒ2-transforms and their applications . Appl. Math. Comput. , 99 : 141 – 151 .
  • Yürekli , O. and Graziadio , C. 1997 . A theorem on the Laplace transform and its applications . Int. J. Math. Ed. Sci. Tech. , 28 : 616 – 621 .
  • Yürekli , O. and Sadek , I. 1991 . A Parseval–Goldstein type theorem on the Widder potential transform and its applications . Int. J. Math. Math. Sci. , 14 : 517 – 524 .
  • Yürekli , O. and Saygınsoy , Ö. 1998 . A theorem on a Laplace-type integral transform and its applications . Int. J. Math. Ed. Sci. Tech. , 29 : 561 – 567 .
  • Yürekli , O. and Wilson , S. 2002 . A new method of solving Bessel's differential equation using the ℒ2-transform . Appl. Math. Comput. , 130 : 587 – 591 .
  • Yürekli , O. and Wilson , S. 2003 . A new method of solving Hermite's differential equation using the ℒ2-transform . Appl. Math. Comput. , 145 : 495 – 500 .

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