Schaum's Outline of Mathematical Handbook of Formulas and Tables by Murray R Spiegel

Author:Murray R Spiegel
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2018-04-06T04:00:00+00:00

Associated Legendre Functions of the First Kind

28.50.

where Pn(x) are Legendre polynomials (page 164). We have

28.51.

28.52.

Special Associated Legendre Functions of the First Kind

28.53.

28.54.

28.55.

28.56.

28.57.

28.58.

Generating Function for (x)

28.59.

Recurrence Formulas

28.60.

28.61.

Orthogonality of (x)

28.62.

28.63.

Orthogonal Series

28.64.

where

28.65.

Associated Legendre Functions of the Second Kind

28.66.

where Qn(x) are Legendre functions of the second kind (page 166).

These functions are unbounded at x = ±1, whereas (x) are bounded at x = ± 1.

The functions satisfy the same recurrence relations as(x) (see 28.60 and 28.61).

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