spherical triangles

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1: 4.42 Solution of Triangles

§4.42 Solution of Triangles

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§4.42(iii) Spherical Triangles

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Figure 4.42.3: Spherical triangle. Magnify

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2: 15.17 Mathematical Applications

… ►The quotient of two solutions of (15.10.1) maps the closed upper half-plane $\mathrm{\Im }z\ge 0$ conformally onto a curvilinear triangle. … ►First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL$(2,ℝ)$, and spherical functions on certain nonsymmetric Gelfand pairs. …

3: 18.1 Notation

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Legendre: $P_n\left(x\right)$.

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Shifted Legendre: $P_n^{\ast }\left(x\right)$.

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Triangle: $P_{m,n}^{\alpha ,\beta ,\gamma }(x,y)$.

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