Abstract

For <i>x</i> / <i>n</i> ≫ 1, the following relations between the Mie-scattering functions <i>a<sub>n</sub></i> (<i>x</i>,<i>m</i>) and <i>b<sub>n</sub></i> (<i>x</i>,<i>m</i>) are satisfied: <i>a</i><sub>1</sub> (<i>x</i>,<i>m</i>)= <i>b</i><sub>2</sub> (<i>x</i>,<i>m</i>)= <i>a</i><sub>3</sub> (<i>x</i>,<i>m</i>) = … = <i>a</i><sub><i>n</i>-1</sub> (<i>x</i>,<i>m</i>) = <i>b<sub>n</sub></i> (<i>x</i>,<i>m</i>) and <i>b</i><sub>1</sub> (<i>x</i>,<i>m</i>) = <i>a</i><sub>2</sub> (<i>x</i>,<i>m</i>)= <i>b</i><sub>3</sub> (<i>x</i>,<i>m</i>) = … = <i>b</i><sub><i>n</i>-1</sub> (<i>x</i>,<i>m</i>) = <i>a<sub>n</sub></i>(<i>x</i>,<i>m</i>) for arbitrary refractive index <i>m</i>. By use of these relations, the Van de Hulst and Deirmendjian conjectures about the <i>x</i> → ∞ behavior of the scattering functions or their linear and bilinear combinations, as well as several new relations, are rigorously proved.

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