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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62741a168dbc4529de44801e/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">Readme_BslRat_ContFr_HillInfDet.doc.doc</div><div class="t m0 x2 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">June 2005</div><div class="t m0 x3 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">Author’s Update in June 2005 :</div><div class="t m0 x3 h3 y5 ff2 fs0 fc0 sc0 ls0 ws0">I have added one more important function Simple_Cont_Frctn_b_1.m which computes<span class="_ _0"></span> a Simple </div><div class="t m0 x3 h3 y6 ff2 fs0 fc0 sc0 ls0 ws0">Continued Fraction by making calls to Continuant_Poly_Kn.m ; in a way, this Programme<span class="_ _0"></span> is a Test </div><div class="t m0 x3 h3 y7 ff2 fs0 fc0 sc0 ls0 ws0">Programme for Continuant_Poly_Kn.m</div><div class="t m0 x3 h3 y8 ff2 fs0 fc0 sc0 ls0 ws0">This suite now lays more emphasis on Simple Continued Fractions.</div><div class="t m0 x3 h3 y9 ff2 fs0 fc0 sc0 ls0 ws0">Accordingly, the Title and Summary put the focus more on Simple Continued Fractions.</div><div class="t m0 x4 h3 ya ff2 fs0 fc0 sc0 ls0 ws0">************</div><div class="t m0 x3 h3 yb ff1 fs0 fc0 sc0 ls0 ws0">Readme_BslRat_ContFr_HillInfDet.doc :</div><div class="t m0 x3 h3 yc ff1 fs0 fc0 sc0 ls0 ws0">First Submission in Mar 2005 :</div><div class="t m0 x3 h3 yd ff1 fs0 fc0 sc0 ls0 ws0">Title<span class="ff2"> : Simple Continued Fractions, Hill's Infinite Determinants, and Bessel Functions' Ratio</span></div><div class="t m0 x3 h3 ye ff1 fs0 fc0 sc0 ls0 ws0">Keywords<span class="ff2"> : Continued Fractions, Hill's Infinite Determinants, Bessel Functions' Ratio</span></div><div class="t m0 x3 h3 yf ff1 fs0 fc0 sc0 ls0 ws0">Summary<span class="ff2"> : Convergence, Simple Continued Fractions, Hill's Infinite Determinants and Bess<span class="_ _0"></span>el </span></div><div class="t m0 x3 h3 y10 ff2 fs0 fc0 sc0 ls0 ws0">Functions' Ratio</div><div class="t m0 x3 h3 y11 ff2 fs0 fc0 sc0 ls0 ws0">************</div><div class="t m0 x3 h3 y12 ff1 fs0 fc0 sc0 ls0 ws0">Update in June 2005 :</div><div class="t m0 x3 h3 y13 ff2 fs0 fc0 sc0 ls0 ws0">A new function : <span class="ff1">Simple_Cont_Frctn_b_1.m</span> has been added which computes a<span class="_ _0"></span> Simple Continued </div><div class="t m0 x3 h3 y14 ff2 fs0 fc0 sc0 ls0 ws0">Fraction by making calls to Continuant_Poly_Kn.m ; in a way, this Programme is a Test<span class="_ _0"></span> Programme </div><div class="t m0 x3 h3 y15 ff2 fs0 fc0 sc0 ls0 ws0">for Continuant_Poly_Kn.m</div><div class="t m0 x3 h3 y16 ff1 fs0 fc0 sc0 ls0 ws0">BslRat_ContFr_HillInfDet.zip<span class="ff2"> is a suite of four *.m files which deal<span class="_ _0"></span> with Convergence, George </span></div><div class="t m0 x3 h3 y17 ff2 fs0 fc0 sc0 ls0 ws0">William Hill's Infinite Determinants, Continued Fractions and Bessel Functions' Ratio.</div><div class="t m0 x3 h3 y18 ff2 fs0 fc0 sc0 ls0 ws0">************</div><div class="t m0 x3 h3 y19 ff1 fs0 fc0 sc0 ls0 ws0">1) Hill_c_Theta_Inf_Det.m<span class="ff2"> "analyses" the Hill Matrix (wrt Infinite D<span class="_ _0"></span>eterminants) as given in :</span></div><div class="t m0 x3 h3 y1a ff2 fs0 fc0 sc0 ls0 ws0">Prob 21, Chapter II, P40 and Chapter 19.42, P415 in :</div><div class="t m0 x3 h3 y1b ff2 fs0 fc0 sc0 ls0 ws0">"A Course in Modern Analysis" by Whittaker and Watson.</div><div class="t m0 x3 h3 y1c ff1 fs0 fc0 sc0 ls0 ws0">2) Continuant_Poly_Kn.m<span class="ff2"> calculates the Continuant Polynomial Kn (x1, x2, ... xn).</span></div><div class="t m0 x3 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0">It is based on Eqn 5 / 4.5.3, P257 and Prob 3, 4.5.3, P373 in Vol 2 of :</div><div class="t m0 x3 h3 y1e ff2 fs0 fc0 sc0 ls0 ws0">"The Art of Computer Programming" by Donald Knuth.</div><div class="t m0 x3 h3 y1f ff1 fs0 fc0 sc0 ls0 ws0">3) Simple_Cont_Frctn_b_1.m<span class="ff2"> is described above.</span></div><div class="t m0 x3 h3 y20 ff1 fs0 fc0 sc0 ls0 ws0">4) Thn_Ellip_BslRat_ContFr_InfDet.m<span class="ff2"> was primarily written to understand<span class="_ _0"></span> the relationship </span></div><div class="t m0 x3 h3 y21 ff2 fs0 fc0 sc0 ls0 ws0">between Bessel Functions, Continued Fractions, Infinite Determinant etc by verifying certain results </div><div class="t m0 x3 h3 y22 ff2 fs0 fc0 sc0 ls0 ws0">of the foll article :</div><div class="t m0 x5 h3 y23 ff2 fs0 fc0 sc0 ls0 ws0">1 / 2</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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