Abstract This paper derives novel finite-sum expressions for the modified Bessel function of the first kind using properties of the Marcum Q function. Limits to infinite sums give expressions that are equivalent but frequently more compact when compared with results in the literature. The finite-sum expressions are also used to re-phrase an inequality for the probability that a sum of independent symmetric random vectors lies in a symmetric convex set not as the sum of two modified Bessel functions of the first kind but via a single function {0}₁F₁ 0 1 F 1.
Dirk Veestraeten (Wed,) studied this question.
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