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Theorems connecting different classes of Self-Reciprocal Functions

Published online by Cambridge University Press:  20 January 2009

Brij Mohan Mehrotra
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1. The question, “How, from a given function which is self-reciprocal for a transform of a particular order, can we construct other functions which are self-reciprocal for transforms of different orders?” was first raised by Hardy and Titchmarsh who gave some rules for constructing such functions. Following their method, I have shown, in a recent paper, that there are certain general theorems of the following type:—

If f (x) is its own Jμtransform, g (x) is its own Jv transform. In this note I add a few more such theorems, the interest lying mainly in the results themselves and not in a rigorous proof thereof; and hence only the formal procedure is given here.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 1 , March 1934 , pp. 53 - 56
Copyright
Copyright © Edinburgh Mathematical Society 1934

References

REFERENCES

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