High Quality Content by WIKIPEDIA articles! In mathematics, the parabolic cylinder functions are special functions defined as solutions to the differential equationThis equation is found, for example, when the technique of separation of variables is used on differential equations which are expressed in parabolic cylindrical coordinates.The above equation may be brought into two distinct forms (A) and (B) by completing the square and rescaling z, called H. F. Weber's equations (Weber 1869):

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