principal%20values
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11—14 of 14 matching pages
11: 25.6 Integer Arguments
12: 12.11 Zeros
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12.11.2
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12.11.3
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►For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii).
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12.11.9
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13: 9.9 Zeros
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►They are denoted by , , , , respectively, arranged in ascending order of absolute value for
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►They lie in the sectors and , and are denoted by , , respectively, in the former sector, and by , , in the conjugate sector, again arranged in ascending order of absolute value (modulus) for See §9.3(ii) for visualizations.
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9.9.6
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9.9.7
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►Tables 9.9.1 and 9.9.2 give 10D values of the first ten real zeros of , , , , together with the associated values of the derivative or the function.
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14: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►In this section we give asymptotic expansions of PCFs for large values of the parameter that are uniform with respect to the variable , when both and
are real.
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►The following expansions hold for large positive real values of , uniformly for .
(For complex values of and see Olver (1959).)
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12.10.33
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