of two variables
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31—40 of 161 matching pages
31: 31.8 Solutions via Quadratures
32: 19.36 Methods of Computation
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►The incomplete integrals and can be computed by successive transformations in which two of the three variables converge quadratically to a common value and the integrals reduce to , accompanied by two quadratically convergent series in the case of ; compare Carlson (1965, §§5,6).
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33: 15.8 Transformations of Variable
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►A quadratic transformation relates two hypergeometric functions, with the variable in one a quadratic function of the variable in the other, possibly combined with a fractional linear transformation.
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34: 18.38 Mathematical Applications
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►This gives also new structures and results in the one-variable case, but the obtained nonsymmetric special functions can now usually be written as a linear combination of two known special functions.
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35: 4.24 Inverse Trigonometric Functions: Further Properties
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►which requires
to lie between the two rectangular hyperbolas given by
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4.24.6
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4.24.7
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4.24.8
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4.24.9
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36: 31.17 Physical Applications
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►The problem of adding three quantum spins , , and can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions.
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37: 4.38 Inverse Hyperbolic Functions: Further Properties
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►which requires
to lie between the two rectangular hyperbolas given by
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4.38.8
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4.38.9
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4.38.11
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4.38.13
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38: 1.13 Differential Equations
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1.13.4
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and belong to domains and respectively, the coefficients and are continuous functions of both variables, and for each fixed (fixed ) the two functions are analytic in (in ).
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39: 31.1 Special Notation
40: Bibliography I
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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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