Are stable distributions smooth enough for each index of stability $alpha$ between 0 and 2, and skewness parameter $beta$ between 0 and 1?

Where there any papers that mention this?

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# Are the family of stable distributions differentiable everywhere on the real line?

Are stable distributions smooth enough for each index of stability $alpha$ between 0 and 2, and skewness parameter $beta$ between 0 and 1?

Where there any papers that mention this?