Formula q_366 (Q253): Difference between revisions

Latest revision as of 13:03, 20 April 2020

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Language	Label	Description	Also known as
English	Formula q_366	No description defined

q_366

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{\begin{vmatrix}(1)\sin(x)&(1)\sin(2x)&(1)\sin(3x)&...&(1)\sin(nx)\\(1)\cos(x)&(2)\cos(2x)&(3)\cos(3x)&...&(n)\cos(nx)\\-(1)^{2}\sin(x)&-(2)^{2}\sin(2x)&-(3)^{2}\sin(3x)&...&-(n)^{2}\sin(nx)\\-(1)^{3}\cos(x)&-(2)^{3}\cos(2x)&-(3)^{3}\cos(3x)&...&-(n)^{3}\cos(nx)\\\end{vmatrix}}

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@@ Property / arqmath formula id @@
+q_366
@@ Property / arqmath formula id: q_366 / rank @@
+Normal rank
@@ Property / Defining formula @@
+ ${\begin{vmatrix}(1)\sin(x)&(1)\sin(2x)&(1)\sin(3x)&...&(1)\sin(nx)\\(1)\cos(x)&(2)\cos(2x)&(3)\cos(3x)&...&(n)\cos(nx)\\-(1)^{2}\sin(x)&-(2)^{2}\sin(2x)&-(3)^{2}\sin(3x)&...&-(n)^{2}\sin(nx)\\-(1)^{3}\cos(x)&-(2)^{3}\cos(2x)&-(3)^{3}\cos(3x)&...&-(n)^{3}\cos(nx)\\\end{vmatrix}}$ 
\begin{vmatrix} (1)\sin(x) & (1)\sin(2x) & (1)\sin(3x) &  ... &   (1)\sin(nx) \\ (1)\cos(x) & (2)\cos(2x) & (3)\cos(3x) &  ... &   (n)\cos(nx) \\  -(1)^2\sin(x) & -(2)^2\sin(2x) & -(3)^2\sin(3x) &  ... &   -(n)^2\sin(nx) \\ -(1)^3\cos(x) & -(2)^3\cos(2x) & -(3)^3\cos(3x) &  ... &   -(n)^3\cos(nx) \\ \end{vmatrix}
+Normal rank