On a singular eigenvalue problem
1968 ◽
Vol 64
(2)
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pp. 439-446
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Keyword(s):
Sears and Titchmarsh (1) have formulated an expansion in eigenfunctions which requires a knowledge of the s-zeros of the equationHere ka > 0 is supposed given and β is a real constant such that 0 ≤ β < π. The above equation is encountered when one seeks the eigenfunctions of the differential equationon the interval 0 < α ≤ r < ∞ subject to the condition of vanishing at r = α. Solutions of (2) are the Bessel functions J±is(kr) and every solution w of (2) is such that r−½w(r) belongs to L2 (α, ∞). Since the problem is of the limit circle type at infinity it is necessary to prescribe a suitable asymptotic condition there to make the eigenfunctions determinate. In the present instance this condition is
1951 ◽
Vol 47
(4)
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pp. 699-712
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1959 ◽
Vol 11
◽
pp. 148-155
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1971 ◽
Vol 69
(2)
◽
pp. 139-148
1970 ◽
Vol 67
(1)
◽
pp. 93-96
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1975 ◽
Vol 72
(3)
◽
pp. 187-193
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Keyword(s):
2006 ◽
Vol 11
(1)
◽
pp. 13-32
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1984 ◽
Vol 99
(1-2)
◽
pp. 51-70
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1986 ◽
Vol 102
(3-4)
◽
pp. 253-257
◽
1964 ◽
Vol 4
(2)
◽
pp. 179-194
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1995 ◽
Vol 36
(4)
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pp. 438-459
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