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The weierstrass-laguerre transform.

H M Srivastava1

  • 1Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada.

Proceedings of the National Academy of Sciences of the United States of America
|March 1, 1971
PubMed
Summary
This summary is machine-generated.

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Researchers derived a novel formula for the product of inverse Weierstrass-Laguerre transforms, utilizing function convolution. This elegant mathematical expression extends to multiple functions, simplifying complex transform analysis.

Area of Science:

  • Mathematical analysis
  • Integral transforms
  • Harmonic analysis

Background:

  • The Weierstrass-Laguerre transform is a specialized integral transform.
  • Understanding products of inverse transforms is crucial for solving differential equations and signal processing.

Purpose of the Study:

  • To derive a simplified expression for the product of inverse Weierstrass-Laguerre transforms.
  • To extend this expression to the product of multiple inverse transforms.

Main Methods:

  • Derivation of an analytical expression.
  • Utilizing the concept of function convolution.
  • Extension of the derived formula.

Main Results:

  • An elegant mathematical expression for the product of two inverse Weierstrass-Laguerre transforms was obtained.

Related Experiment Videos

  • The result is expressed in terms of the convolution of the functions.
  • The main result was successfully generalized for the product of several inverse Weierstrass-Laguerre transforms.

    • Conclusions:

    • The study provides a new, elegant formula for products of inverse Weierstrass-Laguerre transforms.
    • The convolution-based expression simplifies calculations involving multiple transforms.
    • This work offers a valuable tool for researchers in mathematical analysis and related fields.