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defining number type


I would like to simplify certain results by declaring the relevant variables to
take on integer values only. For example:
In[1]:= <<Algebra`SymbolicSum`
In[2]:= Sum[m!/(k! (m-k)!),{k,0,m}]
            m
           2  m!
Out[2]= ------------
        Gamma[1 + m]

and this should simplify to 2^m if m is known to be integer valued. How does one
do this?
Simple minded approaches such as IntegerQ[m]^=True, m /:  IntegerQ[m]=True, or
Declare[m,Integer] don't do it. (In fact Declare.m adds trouble: it somehow
interferes with the Algebra`SymbolicSum` package. After loading both, most
symbolic sums are no longer evaluated, including the one above).

Another question:
how does one implement the operator (x d/dx)^k ?

Thanks,

--
Daniel

Fritz Haber Center for Molecular Dynamics
Hebrew University of Jerusalem








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