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legendre_p-rat

legendre_p(3,rat(x));

Calculate

legendre_p

legendre_p(1,2) ;

Calculate

legendre_p-ratsimp

legendre_p(3, x);

ratsimp(%);

Calculate

legendre_p

%i^2 ;

legendre_p(2,2+5*(%i)) ;

Calculate

legendre_p

legendre_p(2,2+5*%i) ;

Calculate

legendre_p

5*%i^2 ;

legendre_p(2,2+5*(%i)) ;

Calculate

legendre_p

legendre_p(1,71);

Calculate

legendre_p

? legendre_p;

Calculate

legendre_p

legendre_p(m,x);

Calculate

legendre_p

? legendre_p;

Calculate

legendre_p

Run Example
(%i1)legendre_p(383,73);
(%o1) 250630586406020764589493660792579470561734148351847299902542216723647702\
637086996207525339314730343909185386275596966207731720077186372652578466384860\
620421509260990060552466700805452314640732379395919793984406039735172063099687\
455692660538953675039863003175938362544973917946689110200226002272480979544026\
643024421010408001695421541932849175702673959741849803507788051981557986505916\
344384358220435176405305643185805492072784122944246667091934885545612088465167\
721326332574595911931308229662571664543945545576945466142143729210715523505789\
891269967736411022721571307514837456267790132221413809896143842475053390874581\
064515280910752763967359269468726047125639696502533172031363925770469281268976\
993082857491481348770296956673229931665455597078514343678146702401993398779963\
661478634022103915862501751660056963863253997095671297
(%i2) 
Run Example
foo:legendre_p(m,x)*legendre_p(n,x),m=3,n=3;
                                         3             2
                                5 (1 - x)    15 (1 - x)      2
(%o1)            (- 6 (1 - x) - ---------- + ----------- + 1)
                                    2             2
(%i2) integrate(foo,x,-1,1);
                                       2
(%o2)                                  -
                                       7
(%i3) 
Run Example
legendre_p(3, x);
                                         3             2
                                5 (1 - x)    15 (1 - x)
(%o1)             - 6 (1 - x) - ---------- + ----------- + 1
                                    2             2
(%i2) ratsimp(%);
(%o2)             

Related Help

Help for Legendre_p