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Abramovitz presents even and odd solutions to the Weber equation.

He also presents standard solutions as a pair of parabolic cylinder functions.

Clearly any linear combination of the even and odd solutions is also a solution of the equation.

My question is: Why is the parabolic cylinder function so special to be considered a "standard" solution?

He also presents standard solutions as a pair of parabolic cylinder functions.

Clearly any linear combination of the even and odd solutions is also a solution of the equation.

My question is: Why is the parabolic cylinder function so special to be considered a "standard" solution?

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