Jacobi transform

In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials as kernels of the transform .[1][2][3][4]

The Jacobi transform of a function is[5]

The inverse Jacobi transform is given by

Some Jacobi transform pairs

References

  1. Debnath, L. "On Jacobi Transform." Bull. Cal. Math. Soc 55.3 (1963): 113-120.
  2. Debnath, L. "SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY JACOBI TRANSFORM." BULLETIN OF THE CALCUTTA MATHEMATICAL SOCIETY 59.3-4 (1967): 155.
  3. Scott, E. J. "Jacobi transforms." (1953).
  4. Shen, Jie; Wang, Yingwei; Xia, Jianlin (2019). "Fast structured Jacobi-Jacobi transforms". Math. Comp. 88 (318): 1743–1772. doi:10.1090/mcom/3377.
  5. Debnath, Lokenath, and Dambaru Bhatta. Integral transforms and their applications. CRC press, 2014.


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