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11—20 of 253 matching pages
11: 18.21 Hahn Class: Interrelations
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Hahn Krawtchouk
… ►Hahn Meixner
… ►Krawtchouk Charlier
… ►Meixner Charlier
… ►Continuous Hahn Meixner–Pollaczek
…12: 4.31 Special Values and Limits
13: 28.9 Zeros
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►For the zeros of and approach asymptotically the zeros of , and the zeros of and approach asymptotically the zeros of .
…Furthermore, for
and also have purely imaginary zeros that correspond uniquely to the purely imaginary -zeros of (§10.21(i)), and they are asymptotically equal as and .
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14: 19.27 Asymptotic Approximations and Expansions
15: 36.11 Leading-Order Asymptotics
16: 11.11 Asymptotic Expansions of Anger–Weber Functions
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►Then as in
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►If is fixed, and in in such a way that is bounded away from the set of all integers, then
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►as .
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►In particular, as ,
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►Also, as in ,
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17: 22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
18: 6.3 Graphics
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19: 29.5 Special Cases and Limiting Forms
20: 32.11 Asymptotic Approximations for Real Variables
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(b)
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►Conversely, for any nonzero real , there is a unique solution of (32.11.4) that is asymptotic to as .
►If , then exists for all sufficiently large as , and
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►Any nontrivial solution of (32.11.29) that satisfies (32.11.30) is asymptotic to as , where
is a constant.
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►Now suppose .
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If , then oscillates about, and is asymptotic to, as .