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21: Bibliography B
  • R. W. Barnard, K. Pearce, and K. C. Richards (2000) A monotonicity property involving F 2 3 and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.
  • 22: Bibliography M
  • M. E. Muldoon (1977) Higher monotonicity properties of certain Sturm-Liouville functions. V. Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.
  • 23: 1.6 Vectors and Vector-Valued Functions
    A path 𝐜 1 ( t ) , t [ a , b ] , is a reparametrization of 𝐜 ( t ) , t [ a , b ] , if 𝐜 1 ( t ) = 𝐜 ( t ) and t = h ( t ) with h ( t ) differentiable and monotonic. …
    24: 3.11 Approximation Techniques
    Since L 0 = 1 , L n is a monotonically increasing function of n , and (for example) L 1000 = 4.07 , this means that in practice the gain in replacing a truncated Chebyshev-series expansion by the corresponding minimax polynomial approximation is hardly worthwhile. …
    25: 19.29 Reduction of General Elliptic Integrals
    Lastly, define Q ( t 2 ) = f + g t 2 + h t 4 and assume Q ( t 2 ) is positive and monotonic for y < t < x . …
    26: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
    Let T be the self adjoint extension of a formally self-adjoint differential operator of the form (1.18.28) on an unbounded interval X , which we will take as X = [ 0 , + ) , and assume that q ( x ) 0 monotonically as x , and that the eigenfunctions are non-vanishing but bounded in this same limit. …