relations to trigonometric functions
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11: 19.25 Relations to Other Functions
§19.25 Relations to Other Functions
… ►§19.25(iv) Theta Functions
… ► … ►§19.25(vii) Hypergeometric Function
… ►12: 13.18 Relations to Other Functions
§13.18 Relations to Other Functions
►§13.18(i) Elementary Functions
… ►§13.18(iv) Parabolic Cylinder Functions
… ►§13.18(v) Orthogonal Polynomials
… ►Laguerre Polynomials
…13: 19.10 Relations to Other Functions
§19.10 Relations to Other Functions
►§19.10(i) Theta and Elliptic Functions
►For relations of Legendre’s integrals to theta functions, Jacobian functions, and Weierstrass functions, see §§20.9(i), 22.15(ii), and 23.6(iv), respectively. … ►§19.10(ii) Elementary Functions
… ►For relations to the Gudermannian function and its inverse (§4.23(viii)), see (19.6.8) and …14: 19.6 Special Cases
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19.6.8
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15: 22.16 Related Functions
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22.16.8
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16: 7.2 Definitions
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§7.2(i) Error Functions
… ► , , and are entire functions of , as is in the next subsection. ►Values at Infinity
… ► , , and are entire functions of , as are and in the next subsection. … ►§7.2(iv) Auxiliary Functions
…17: 28.32 Mathematical Applications
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►If the boundary conditions in a physical problem relate to the perimeter of an ellipse, then elliptical coordinates are convenient.
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►This leads to integral equations and an integral relation between the solutions of Mathieu’s equation (setting , in (28.32.3)).
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►approaches the same value when tends to the endpoints of .
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►Two conditions are used to determine .
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18: 24.15 Related Sequences of Numbers
§24.15 Related Sequences of Numbers
►§24.15(i) Genocchi Numbers
… ►§24.15(ii) Tangent Numbers
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24.15.3
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§24.15(iii) Stirling Numbers
…19: 18.35 Pollaczek Polynomials
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18.35.7
, .
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