MaplePrimes - answers and comments on Question, how to evaluate to this equation

It is impossible

Markiyan Hirnyk — Wed, 06 Feb 2013 17:34:27 Z

because the Laguerre functions are not polynomials in contradistinction from the generalized Laguerre polynomials.

if it is impossible, how arthur derive this?

williamov — Wed, 06 Feb 2013 18:50:32 Z

if it is impossible, how Author derive this? need transformation?

i see that they are quite similar, like just need a few more steps, then success

can it be manually done by observation using below script

restart;
n := 1:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues1 := factor(simplify(rodrigues));
n := 2:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues2 := factor(simplify(rodrigues));
n := 3:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues3 := factor(simplify(rodrigues));

                          -(4 p - 3) p
                    1   /    2            \
                    - p \16 p - 40 p + 15/
                    4
               1    /    3        2              \
             - -- p \64 p - 336 p + 420 p - 105/
               24

Your outputs are not formulas (5.9)

Markiyan Hirnyk — Wed, 06 Feb 2013 20:31:28 Z

@williamov This is not (5.9).

when try to reverse find back alpha and x

williamov — Fri, 08 Feb 2013 17:08:23 Z

when try to reverse find back alpha and x from existing equations

x and alpha are very complex

solve({sqrt(2*p)*exp(-p*t) = exp(x)*(x^(-alpha))/0!*exp(-x)*(x^(0+alpha)), sqrt(2*p)*(-2*p*t+1)*exp(-p*t) = exp(x)*(x^(-alpha))/1!*diff(exp(-x)*(x^(1+alpha)), x$1)},{alpha,x});

i still suspect this rodrigue formula is the source