What is the function of C3?

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C2 and C3 are recommended to prevent oscillation of the LM317 and somewhat improving transient response. The datasheet specifies .1uf for both of them.
 

Thank you very much
How it is somewhat improving transient response?
 

The LM317 does not respond immediately to a transient: an input voltage change or an output current change. It has a small delay. Then the output has a voltage spike that is reduced by the output capacitor as shown on its datasheet that you should look at!
 

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