A modified spherical Bessel function of the second kind, also called a "spherical modified Bessel function of the first kind" or (regrettably) a "modified spherical Bessel function of the third kind", is the second solution to the modified spherical Bessel differential equation, given by k_n(x) congruent sqrt(2/(π x))K_(n + 1/2)(x), where K_n(z) is a modified Bessel function of the second kind For positive x, the first few values for small nonnegative integer indices are
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