Formal sum

In mathematics, a formal sum, formal series, or formal linear combination may be:

• In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients.
• In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients.
• In the study of series (mathematics), a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum converges.
• In the study of power series, a sum of infinitely many monomials with distinct positive integer exponents, again considered as an abstract object regardless of convergence.

.mw-parser-output .dmbox{display:flex;align-items:center;clear:both;margin:0.9em 1em;border-top:1px solid #ccc;border-bottom:1px solid #ccc;padding:0.25em 0.35em;font-style:italic}.mw-parser-output .dmbox>*{flex-shrink:0;margin:0 0.25em}.mw-parser-output .dmbox-body{flex-grow:1;flex-shrink:1;padding:0.1em 0}.mw-parser-output .dmbox-invalid-type{text-align:center}