THE RODRIGUES OPERATOR TRANSFORM, PRELIMINARY REPORT.
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
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The generalized Rodrigues operators introduced include fractional integrals and the Laplace transform. All of the commonly treated special functions can be expressed in terms of these operators. Moreover, the recurrence, differentiation and transformation relations as well as the interrelations with other functions become immediate simple consequences of the calculus of the Rodrigues operators. Using the generalized Parseval relations a great many known integral transforms can be stated as a chain of Rodrigues operators. These include the Hankel, Stieljes, modified Bessel, Neumann, Legendre and hypergeometric transforms. The Rodrigues operators provide a clarification of the essential structure which unifies the relations of integral transforms, special functions and differential operators. This insight yields a technique whereby a new transform or chain of transforms can be tailor made to deal with an arbitrary differential operator. This method has application in a large number of boundary value problems of mathematical physics. Author
- Numerical Mathematics