values at infinity
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1: 7.2 Definitions
2: 6.2 Definitions and Interrelations
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Values at Infinity
…3: 6.4 Analytic Continuation
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►Analytic continuation of the principal value of yields a multi-valued function with branch points at
and .
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4: 4.23 Inverse Trigonometric Functions
5: 12.14 The Function
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and form a numerically satisfactory pair of solutions when .
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§12.14(ii) Values at and Wronskian
… ►These follow from the contour integrals of §12.5(ii), which are valid for general complex values of the argument and parameter . … ►Then as … ►Negative ,
…6: 10.9 Integral Representations
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►Also, is continuous on the path, and takes its principal value at the intersection with the interval .
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7: 4.17 Special Values and Limits
§4.17 Special Values and Limits
► …8: 4.31 Special Values and Limits
§4.31 Special Values and Limits
► …9: 3.6 Linear Difference Equations
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►If, as , the wanted solution grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (backward) recursion is stable.
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►The least value of that satisfies (3.6.9) is found to be 16.
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►For a difference equation of order (),
…Typically conditions are prescribed at the beginning of the range, and conditions at the end.
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