Digital Library of Mathematical Functions
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28 Mathieu Functions and Hill’s EquationMathieu Functions of Noninteger Order

§28.16 Asymptotic Expansions for Large q

Let s=2m+1, m=0,1,2,, and ν be fixed with m<ν<m+1. Then as h(=q)+

28.16.1 λν(h2)-2h2+2sh-18(s2+1)-127h(s3+3s)-1212h2(5s4+34s2+9)-1217h3(33s5+410s3+405s)-1220h4(63s6+1260s4+2943s2+486)-1225h5(527s7+15617s5+69001s3+41607s)+.

For graphical interpretation, see Figures 28.13.1 and 28.13.2.

See also §28.8(iv).