DLMF:13.21.E12 (Q4620): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.21.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sqrt{\kappa\zeta-4\mu^{2}}-2\mu\operatorname{% arctan}\left(\frac{\sqrt{\kappa\zeta-4\mu^{2}}}{2\mu}\right)=\tfrac{1}{2}(X-% \pi\mu)-\mu\operatorname{arctan}\left(\frac{x\kappa-2\mu^{2}}{\mu X}\right)+% \kappa\operatorname{arcsin}\left(\frac{X}{2\sqrt{\kappa^{2}-\mu^{2}}}\right),}}

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DLMF:13.21.E12

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{\displaystyle{\displaystyle 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}\leq x<2\kappa+% 2\sqrt{\kappa^{2}-\mu^{2}}}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

C4.S23.SS2.p1.m5adec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7adec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1jdec

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