Establish the following formulas for the function defined for all .
 .
 .
 .
 .
 .
 .

Proof.
and ; hence, , for all 
Proof.
for all 
Proof.
, valid for all 
Proof.
, valid for all 
Proof.
and . This is valid for all 
Proof.
valid for all
Establish the following formulas for the function defined for all .