catch SciMax Toolbox cbffac

SciMax Toolbox >> cauchysum

cauchysum

Option variable

cauchysum

Description

Default value: false

When multiplying together sums with inf as their upper limit, if sumexpand is true and cauchysum is true then the Cauchy product will be used rather than the usual product. In the Cauchy product the index of the inner summation is a function of the index of the outer one rather than varying independently.

Example:

(%i1) sumexpand: false$
(%i2) cauchysum: false$
(%i3) s: sum (f(i), i, 0, inf) * sum (g(j), j, 0, inf);
                      inf         inf
                      ====        ====
                      \           \
(%o3)                ( >    f(i))  >    g(j)
                      /           /
                      ====        ====
                      i = 0       j = 0
(%i4) sumexpand: true$
(%i5) cauchysum: true$
(%i6) ''s;
                 inf     i1
                 ====   ====
                 \      \
(%o6)             >      >     g(i1 - i2) f(i2)
                 /      /
                 ====   ====
                 i1 = 0 i2 = 0
catch SciMax Toolbox cbffac