Abstract
UNTIL recently the only tables of the associated Legendre functions Pmn (x) were those of Tallqwist (Helsingfors, 1906), who calculated them for values of n and m up to 8 and for values of x from 0.00 to 1.00. As the function vanishes when the positive integer n is less than the positive integer m, Tallqwist's tables contained 3,600 entries. He calculated functions of even order exactly, and those of odd order with an accuracy varying from four to ten decimal places. Now the Fouad I University at Cairo has provided a much more extensive table, for values of n and m up to 10, and for values of x from 0.000 to 1.000. The entries have been obtained correct to 8 decimal places, except for n = 9, 10 and m equal to or greater than 5, where, as the entries are large, the values have been calculated to four decimal places only. Parts of the tables have been checked by Dr. L. J. Comrie, whose knowledge and experience of mathematical tables are exceptionally wide.
Tables of Legendre Associated Functions
Zaki
Mursi
By. (Fouad I University: Faculty of Science, Publication No. 4.) Pp. viii + 286. (Cairo: Fouad I University, 1941.)
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Tables of Legendre Associated Functions. Nature 152, 399 (1943). https://doi.org/10.1038/152399d0
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DOI: https://doi.org/10.1038/152399d0