### The Maxima on-line user's manual

Algebra Calculator

#### Cauchysum

-- Option variable: cauchysum 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

(%o1)                                true
(%i2)

### Related Examples

##### cauchysum-false-inf-sumexpand-true

sumexpand: false;

cauchysum: false;

s: sum (f(i), i, 0, ...

Calculate

cauchysum:true;

sumexpand:false;

gensumnum:0;

Calculate

##### cauchysum-false-inf-sumexpand-true

sumexpand: false;

cauchysum: false;

s: sum (i*q^i, i, 0,...

Calculate

##### cauchysum-false-intosum-simpsum-sum-sumcontract-sumexpand-true

a: sum(a[k], k, 1, 10...

b: sum(b[k], k, 1, 10...

sum(a+b, k, 1, 10);

Calculate

cauchysum:false;

psexpand:false;

simpproduct:true;

Calculate

##### cauchysum-false-gensumnum-inf-intosum-psexpand-sumcontract-sumexpand-true

cauchysum:true;

psexpand:false;

simpproduct:trie;

Calculate

##### cauchysum-sum

sum ( (x-2)^n*2^(1-n)...

Calculate

##### cauchysum-false-gensumnum-inf-intosum-psexpand-sumcontract-sumexpand-true

cauchysum:true;

psexpand:false;

simpproduct:trie;

Calculate

##### cauchysum-factor-false-gensumnum-inf-intosum-psexpand-sumcontract-sumexpand-true

cauchysum:true;

psexpand:false;

simpproduct:true;

Calculate

##### cauchysum-intosum-simpsum-sum-sumcontract-true

a: sum(a[k], k, 1, 10...

b: sum(b[k], k, 1, 10...

sum(a+b, k, 1, 10);

Calculate