# §28.35 Tables

## §28.35(i) Real Variables

• Blanch and Clemm (1962) includes values of and for with , . Also and for with , . Precision is generally 7D.

• Blanch and Clemm (1965) includes values of , for , ; , . Also , for , ; , . In all cases . Precision is generally 7D. Approximate formulas and graphs are also included.

• Blanch and Rhodes (1955) includes , , , ; 8D. The range of is 0 to 0.1, with step sizes ranging from 0.002 down to 0.00025. Notation: , .

• 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.

• Stratton et al. (1941) includes , , and the corresponding Fourier coefficients for and for or , . Precision is mostly 5S. Notation: , , , and for , see §28.1.

• 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.

## §28.35(ii) Complex Variables

• Blanch and Clemm (1969) includes eigenvalues , for , , , ; 4D. Also and for , , and , respectively; 8D. Double points for ; 8D. Graphs are included.

## §28.35(iii) Zeros

• Blanch and Clemm (1965) includes the first and second zeros of , for , and , for , with ; 7D.

• Ince (1932) includes the first zero for , for or 6, ; 4D. This reference also gives zeros of the first derivatives, together with expansions for small .

• Zhang and Jin (1996, pp. 533–535) includes the zeros (in degrees) of , for , and the first 5 zeros of , for or , . Precision is mostly 9S.

## §28.35(iv) Further Tables

For other tables prior to 1961 see Fletcher et al. (1962, §2.2) and Lebedev and Fedorova (1960, Chapter 11).