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J. Math. Phys. 28, 8 (1987); http://dx.doi.org/10.1063/1.527758 (7 pages)
On classical theory of moments: Finite‐set‐of‐moments approach. I. Non‐negative distribution: Its even moments and Hankel transform
(Received 16 May 1985; accepted 10 September 1986)
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Add to FacebookFor an unknown non‐negative distribution Ω(z), the corresponding Hankel transform F(k) is introduced. It is proposed to partition F(k) in such a way that each component satisfies a linear differential relation whose solution gives an approximate Hankel transform in terms of a given finite set of even moments. As a result, for a known finite set of even moments, the non‐negative distribution Ω(z) is obtained in the form of a finite sum of the definite differential and integral forms of the Gaussian distributions.
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C. T. Corcoran and P. W. Langhoff, J. Math. Phys. 18, 651 (1977JMAPAQ000018000004000651000001).
L. R. Mead and N. Papanicolaou, J. Math. Phys. 25, 2404 (1984JMAPAQ000025000008002404000001).
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