ActiveUser

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7 years, 117 days
i would also not like to ask, but if not ask, what should i do?

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These are replies submitted by ActiveUser

when a comment, this site has error in firefox and i.e.

now become normal

@Preben Alsholm 

i find pochhammer can be converted to n! * binomial(n,k)

http://en.wikipedia.org/wiki/Pochhammer_symbol

i just close my computer,

if you tried, tell me whether the summation containing binomial be simplified to a correct generating function

 

if not, any other transformation formula can simplify to remove binomial in summation

@Preben Alsholm 

i find pochhammer can be converted to n! * binomial(n,k)

http://en.wikipedia.org/wiki/Pochhammer_symbol

i just close my computer,

if you tried, tell me whether the summation containing binomial be simplified to a correct generating function

 

if not, any other transformation formula can simplify to remove binomial in summation

@Preben Alsholm 

i use this to further calculate the generating function, it is not the official one.

Hermit

restart;
with(gfun):
test4 := diff(P(x),x$2)-2*x*diff(P(x),x)+2*n*P(x)=0;
sol := dsolve(test4);
series(rhs(sol),x,2);
sol2 := eval(rhs(sol), [_C2 = 0, _C1 = 1]);
convert(sol2, hypergeom);

restart;
with(SumTools):
An := 1/2-1/2*n;
Cn := 3/2;
An2 := 1/2-1/2*n+L;
Cn2 := 3/2+L;
gen := Summation(Product(An2, L=0..k-1)/Product(Cn2, L=0..k-1)/k!*z^k, k=0..infinity);
gen := Summation(pochhammer(An,k)/pochhammer(Cn,k)/k!*z^k, k=0..infinity);
genfun := simplify(gen);
correct_genfun := exp(2*x*z-z^2);

@Preben Alsholm 

i use this to further calculate the generating function, it is not the official one.

Hermit

restart;
with(gfun):
test4 := diff(P(x),x$2)-2*x*diff(P(x),x)+2*n*P(x)=0;
sol := dsolve(test4);
series(rhs(sol),x,2);
sol2 := eval(rhs(sol), [_C2 = 0, _C1 = 1]);
convert(sol2, hypergeom);

restart;
with(SumTools):
An := 1/2-1/2*n;
Cn := 3/2;
An2 := 1/2-1/2*n+L;
Cn2 := 3/2+L;
gen := Summation(Product(An2, L=0..k-1)/Product(Cn2, L=0..k-1)/k!*z^k, k=0..infinity);
gen := Summation(pochhammer(An,k)/pochhammer(Cn,k)/k!*z^k, k=0..infinity);
genfun := simplify(gen);
correct_genfun := exp(2*x*z-z^2);

@Carl Love 

http://en.wikipedia.org/wiki/Charlier_polynomials

compare with above, i guess a is mu, two structures of genfun are totally different.

even change to pochhammer, can not summation

@Markiyan Hirnyk 

not tired, want a smooth operation in this, i am not a physics graduate, not sure manually convert without maple, i do not have confidence to be sure whether is correct or not.

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