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Generalised Algebraic Continued Fractions related to Definite Integrals1

Published online by Cambridge University Press:  20 January 2009

L. R. Shenton
L. R. Shenton
Affiliation:
Manchester College of Science and Technology, Manchester, 1.
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The present paper is a continuation of the work initiated in [l]-[5]. In [5] I gave an expansion of the form

for the second order C.F. associated with

where U8, V8, W8 satisfy a fourth-order recurrence relation, there being a similar expansion for third order C.F.'s. I shall now give simple expressions for U8, V8, W8 (or related forms) in terms of χ2s(Z1), χ2s (Z2), ω2s(Z1), ω2s(Z2), where

and show that there is a remarkable relation between the recurrence formula for the first order C.F. and that satisfied by U3, V3, W3. The generalised form of these results will be stated and proved.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 4 , May 1958 , pp. 170 - 182
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

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