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exp(’A/x) [Laguerre] Misleading title; Elliott-Tuan[127]
Contour integrals for ”Fourier” coe¬cients are
arbitrary f(x) Jacobi,Laguerre & Hermite coe¬s.

Stieltjes Functions Upper Bound on β Boyd[49]

Lower Bound: β ≥ 1 ’ r/2
Stieltjes Functions Boyd[49]

General Hermite functions Boyd[48, 52]

General Rational Chebyshev Boyd[50, 53, 54]

General Fourier & Chebyshev Boyd (1990c)[59]
error envelopes

Entire Functions Chebyshev Ciasullo-Cochran[99]

General Mapped Fourier Cloot-Weideman[102],
for In¬nite Interval Weideman-Cloot[312]

Entire Functions: Fourier coe¬s. Boyd[64]
Exp(Gaussian)

Error Function Rational Chebyshev series Weideman[309, 310, 311]




ActaApplFINAL_OP92.tex; 21/08/2000; 16:16; no v.; p.109
110 John P. Boyd




Table VI. A Maple program to compute the Chebyshev-„ approximation for the
Stieltjes function S(x)

# For brevity, epsilon is replaced by x
M:= 8; M1:=M+1; # degree of Chebyshev polynomial
# Next, compute the shifted Chebyshev polynomial TN
T[0]:=1; T[1]:=2*y - 1;
for j from 2 by 1 to M do T[j]:=2*(2*y-1)*T[j-1]-T[j-2]; od;
y:=x/z; TM:=simplify(T[M]);
S:=a0; for j from 1 by 1 to N do S:=S+a.j*x**j; od;
resid:=x*x*di¬(S,x) + (1+x)*S - 1 - tau*TM; resid:=collect(resid,x);
for j from 0 by 1 to M1 do eq.j:=coe¬(resid,x,j); od;
eqset:=eq.(0..M1); varset:=tau,a.(0..M); asol:=solve(eqset,varset); assign(asol);
x:=z; Srational:=simplify(S);




ActaApplFINAL_OP92.tex; 21/08/2000; 16:16; no v.; p.110

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