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The summation symbol. Mathematical notation uses a symbol that compactly represents summation of many similar terms: the summation symbol, , an enlarged form of the upright capital Greek letter sigma. [1] This is defined as
the Christoffel symbols that describe components of a metric connection; the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine; the Feferman–Schütte ordinal Γ 0; represents: the specific weight of substances; the lower incomplete gamma function
u+03fe Ͼ greek capital dotted lunate sigma symbol; u+03ff Ͽ greek capital reversed dotted lunate sigma symbol; u+2140 ⅀ double-struck n-ary summation; u+2211 ∑ n-ary summation (∑, ∑) u+23b2 ⎲ summation top [a] u+23b3 ⎳ summation bottom; u+2ca4 Ⲥ coptic capital letter sima; u+2ca5 ⲥ coptic small letter sima; u+2cea ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
An index that is summed over is a summation index, in this case "i ". It is also called a dummy index since any symbol can replace "i " without changing the meaning of the expression (provided that it does not collide with other index symbols in the same term). An index that is not summed over is a free index and should appear only once per ...
The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
Summation notation may refer to: Capital-sigma notation, mathematical symbol for summation; Einstein notation, summation over like-subscripted indices
Using the symbols , for the partial sums of the original series and , for the partial sums of the series after multiplication by , this definition implies that , =, for all , and therefore also , =,, when the limits exist. Therefore if a series is summable, any nonzero scalar multiple of the series is also summable and vice versa: if a series ...