1—10 of 35 matching pages
1: 28.4 Fourier Series
§28.4(ii) Recurrence Relations… ►
§28.4(iii) Normalization… ►
§28.4(v) Change of Sign of… ►
§28.4(vi) Behavior for Small… ►
§28.4(vii) Asymptotic Forms for Large…
2: 28.11 Expansions in Series of Mathieu Functions
3: 28.35 Tables
§28.35 Tables… ►
Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
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.
Blanch and Clemm (1969) includes eigenvalues , for , , , ; 4D. Also and for , , and , respectively; 8D. Double points for ; 8D. Graphs are included.
4: 28.14 Fourier Series
5: 28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions
6: 28.10 Integral Equations
7: 28.15 Expansions for Small
§28.15 Expansions for Small…
8: 28.23 Expansions in Series of Bessel Functions
9: 29.20 Methods of Computation
… ►Subsequently, formulas typified by (29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by backward recursion followed by application of formulas typified by (29.6.5) and (29.6.6) to achieve normalization; compare §3.6. … ►A third method is to approximate eigenvalues and Fourier coefficients of Lamé functions by eigenvalues and eigenvectors of finite matrices using the methods of §§3.2(vi) and 3.8(iv). … ►The corresponding eigenvectors yield the coefficients in the finite Fourier series for Lamé polynomials. …