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21: 28.2 Definitions and Basic Properties
§28.2(vi) Eigenfunctions
…22: 25.11 Hurwitz Zeta Function
23: 27.15 Chinese Remainder Theorem
24: 26.10 Integer Partitions: Other Restrictions
§26.10 Integer Partitions: Other Restrictions
►§26.10(i) Definitions
… ► denotes the number of partitions of into parts with difference at least . denotes the number of partitions of into parts with difference at least 3, except that multiples of 3 must differ by at least 6. … ►25: 26.3 Lattice Paths: Binomial Coefficients
26: 28.35 Tables
Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
Kirkpatrick (1960) contains tables of the modified functions , for , , ; 4D or 5D.
National Bureau of Standards (1967) includes the eigenvalues , for with , and with ; Fourier coefficients for and for , , respectively, and various values of in the interval ; joining factors , for with (but in a different notation). Also, eigenvalues for large values of . Precision is generally 8D.
Zhang and Jin (1996, pp. 521–532) includes the eigenvalues , for , ; (’s) or 19 (’s), . Fourier coefficients for , , . Mathieu functions , , and their first -derivatives for , . Modified Mathieu functions , , and their first -derivatives for , , . Precision is mostly 9S.
27: 26.12 Plane Partitions
28: 21.1 Special Notation
positive integers. | |
( times). | |
… | |
set of all matrices with integer elements. | |
… | |
set of all elements of , modulo elements of . Thus two elements of are equivalent if they are both in and their difference is in . (For an example see §20.12(ii).) | |
intersection index of and , two cycles lying on a closed surface. if and do not intersect. Otherwise gets an additive contribution from every intersection point. This contribution is if the basis of the tangent vectors of the and cycles (§21.7(i)) at the point of intersection is positively oriented; otherwise it is . | |
… |
29: 12.1 Special Notation
real variables. | |
… | |
nonnegative integers. | |
… |