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1. H-Transforms. - London: Charman and Hall, 2004. - 390 p.

2. .., .. . - .: , 1961. - 524 .

3. ., . . - .: , 1968. - .1. - 344 .

4. ³ . (-) . - .: "", 2009. - 476 .

5. The use of integral transforms. - New York: McGraw-Hill Book Comp., 1972. - 539 p.

6. Integral Transforms and Their Applications. - Boca Raton: CRC Press, 1995. - 456 p.

7. A theorem on Stieltjes-type integral transforms and its applications// Complex Var. Theory Appl.- 1995. - . - P. 159-168.

8. On the generalized confluent hypergeometric function and its applications// J. "Fractional Calculus and Appl. Anal. - 2006. - , N 2. - P.101-108.

9. ., . . - .: , 1965. - .1. - 296 .

10. ³ .., .. // "ϲ". - 2008. - 6(62). - . 133-137.

 


. ³

,

, , Widder . - . , -. .

 

 

N. Virchenko

On new generalizations of the classical integral transforms

This paper is devoted to the theory of the new integral transforms, generalizing the classical Laplace, Stieltjes, Widder potential integral transforms. The - generalized confluent hypergeometric functions are the kernels of these integral transforms. Inverse formulae for new integral transforms are proved. The relations of Parseval-Goldstein type are established. Some examples of applications of the new integral transforms are given.

 

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