Hermite polynomials
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1: 18.3 Definitions
§18.3 Definitions
►Table 18.3.1 provides the definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and normalization (§§18.2(i) and 18.2(iii)). … ►Name | Constraints | ||||||
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Hermite | |||||||
Hermite |
2: 18.41 Tables
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►For () see §14.33.
►Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates , , , and for .
The ranges of are for and , and for and .
The precision is 10D, except for which is 6-11S.
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►For , , and see §3.5(v).
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3: 7.10 Derivatives
4: 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 .
Here denotes the Hermite polynomial of degree (§18.3).
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5: 18.38 Mathematical Applications
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Integrable Systems
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18.38.1
►with as in §18.3, satisfies the Toda equation
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