Frequency scaling property for Fourier series

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For Fourier transform, there is an equation connecting time-scaling with frequency-scaling. (By scaling, I mean multiplying by constant for time or frequency)

Is there such a relation for Fourier series that is not just Fourier transform relation?

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Time scaling a periodic signal changes its periodicity by the Fourier coefficients remain intact. Please see http://web.mit.edu/shou/www/6.003/tutorial_tables.pdf