Skip to main content
×
×
Home

Notes on special systems of orthogonal Functions (III): A System of orthogonal polynomials

  • G. H. Hardy (a1)
Extract

Generalities. Suppose that

is real and L2(0, ∞), that

is its Mellin transform, and that

Then K(1)(x) generates a “Watson transformation”, with a “Fourier theorem”

valid for every F(x) of L2(0, ∞).

Copyright
References
Hide All
(1)Bateman, H.Some properties of a certain set of polynomials”. Tóhoku math. J. 37 (1933), 23–8.
(2)Bateman, H.The polynomial F n(x)”. Annals of math. 35 (1934), 767–75.
(3)Hardy, G. H.Notes on some points in the integral calculus (46–47)”. Messenger of math. 46 (1917), 175–82, and 47 (1918), 81–8.
(4)Titchmarsh, E. C.Theory of Fourier integrals (Oxford, 1937).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed