Some properties for ν-zeros of parabolic cylinder functions
Abstract
Let Dν(z) be the Parabolic Cylinder function. We study the ν-zeros of the function ν → Dν(z) with respect to the real variable z. We establish a formula for the derivative of a zero and deduce some monotonicity results. Then we also give an asymptotic expansion for ν-zeros for large positive z.
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