Chebyshev polynomial expansion of Bose-Einstein functions of orders $1$ to $10$
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چکیده
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extensions of some polynomial inequalities to the polar derivative
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15 صفحه اولExpansion of a coherent array of Bose-Einstein condensates.
We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their r...
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The theorem proved here extends the author's previous work on Chebyshev series [4] by showing that if f(x) is a member of the class of so-called "Stieltjes functions" whose asymptotic power series 2 anx" about x = 0 is such that ttlogjaj _ hm —;-= r, «log n then the coefficients of the series of shifted Chebyshev polynomials on x e [0, a],2b„Tf(x/a), satisfy the inequality 2 . m log | (log |M) ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1969
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1969-0247739-x