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A generalization of the polylogarithm function defined by S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt. The function reduces to the usual ...

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1. Particular cases include sin(pi) = 0 (1) sin(pi/2) = 1 (2) ...

A ring is called left (respectively, right) Noetherian if it does not contain an infinite ascending chain of left (respectively, right) ideals. In this case, the ring in ...

A graphical plot which can be used for solving certain types of equations. According to Steinhaus (1999, p. 301), the Nomogram was invented by the French mathematicians ...

A non-Abelian group, also sometimes known as a noncommutative group, is a group some of whose elements do not commute. The simplest non-Abelian group is the dihedral group ...

The following table gives the number of nonadjacent vertex pairs k on graphs of n=1, 2, ... vertices. k counts 1 0, 1, 1, 1, 1, 1, 1, ... 2 0, 0, 1, 2, 2, 2, 2, ... 3 0, 0, ...

A number which is simultaneously a nonagonal number N_m and heptagonal number Hep_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=1/2n(5n-4). (1) Completing the ...