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21—30 of 55 matching pages
21: 26.14 Permutations: Order Notation
22: 9.7 Asymptotic Expansions
§9.7 Asymptotic Expansions
… ►Numerical values of are given in Table 9.7.1 for to 2D. … ►§9.7(iii) Error Bounds for Real Variables
… ►§9.7(iv) Error Bounds for Complex Variables
… ►23: 15.10 Hypergeometric Differential Equation
Singularity
… ►Singularity
… ►Singularity
… ►The connection formulas for the principal branches of Kummer’s solutions are: … ►24: 36.4 Bifurcation Sets
25: Bibliography F
26: Bibliography N
27: 32.8 Rational Solutions
28: 5.11 Asymptotic Expansions
§5.11(ii) Error Bounds and Exponential Improvement
… ►For re-expansions of the remainder terms in (5.11.1) and (5.11.3) in series of incomplete gamma functions with exponential improvement (§2.11(iii)) in the asymptotic expansions, see Berry (1991), Boyd (1994), and Paris and Kaminski (2001, §6.4). … ►29: Bibliography M
30: 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.
Blanch and Clemm (1969) includes eigenvalues , for , , , ; 4D. Also and for , , and , respectively; 8D. Double points for ; 8D. Graphs are included.