When is the Modified Bessel Function Equal to Its Derivative? (I. Nasell)
نویسندگان
چکیده
منابع مشابه
When Is 0.999... Equal to 1?
where Hj := ∑ j i=1(1/ i) are the harmonic numbers. This question in the title is beyond the scope of a mathematics journal. There are, however, mathematical papers proving identities that were discovered because numerical computation pointed to a simple answer. The anecdotal evidence then accumulates in a misleading manner: when the conjectured identity is false we are less likely ever to know...
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15 صفحه اولOn the Computation of Certain Integrals Containing the Modified Bessel Function I 0 ( £ )
Efficient stratagems are developed for numerically evaluating oneand two-dimensional integrals over x, y with integrand exp( — x — y)I0(2Jpxy ). The integrals are expressed in terms of convergent series, which exhibit the correct limiting behavior, and which can be evaluated recursively. The performances of these stratagems are compared with numerical integration.
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In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient cond...
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One can’t do mathematics for more than ten minutes without grappling, in some way or other, with the slippery notion of equality. Slippery, because the way in which objects are presented to us hardly ever, perhaps never, immediately tells us–without further commentary–when two of them are to be considered equal. We even see this, for example, if we try to define real numbers as decimals, and th...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 1978
ISSN: 0036-1445,1095-7200
DOI: 10.1137/1020114