(* Copyright INRIA and Microsoft Corporation, 2008-2013. *)(* DDMF is distributed under CeCILL-B license. *)INCLUDE"preamble.ml"letitalic s =DC.dstyle (DC.css_of_string"font-style: italic") sletglossary =(* Please, keep the notions alphabetically sorted. *)[ ("ansatz", (<:text<\An$(italic"ansatz") is an expressionforthe general solutions \ofa problem,orformostofthem, which typically involves \ undetermined coefficients,andis usedforan educated guess.\ >>)) ; ("Chebyshev expansion", (<:text<\A$(italic"Chebyshev expansion") is a seriesofthe form \ <:imath<f(x)=\frac{c_0}{2}+\sum_{n=1}^{+\infty} c_nT_n(x)>> \ where <:imath<T_n(x)>> denotes the <:imath<n>>thChebyshevpolynomial \ofthe first kind.\ >>)) ; ("formal power series", (<:text<\A$(italic"formal power series") <:imath<f(x)>> is an infinite sum \ofthe form <:imath<\sum_{n = 0}^\infty f_n x^n>> \ where the <:imath<f_n>> areinsome common ring <:imath<R>>. \Thecoefficient <:imath<f_n>>of<:imath<x^n>>in<:imath<f(x)>> \ is also denoted <:imath<[x^n] \, f(x)>>. \Theringofformal power series is denoted <:imath<R[[x]]>>.\ >>)) ; ("formal logarithmic sum", (<:text<\A$(italic"formal logarithmic sum") is a finite sumofthe form \ <:imath<\sum_{\alpha,j} x^\alpha f_{\alpha,j}(x) \log(x)^j>> \ where the <:imath<\alpha>> areinsome common ring <:imath<R>> \andthe <:imath<f_{\alpha,j}(x)>> are formal power series \in<:imath<R[[x]]>>.\ >>)) ; ("indicial equation", (<:text<\The$(italic"indicial equation") (or$(italic"indicial polynomial")) \ofa linear differential equationwithpolynomial coefficients is the \ coefficientofthe power of_<:imath<x>>withlowest exponent \inthe expression that is obtained by the substitution \ <:imath<y(x) = x^\alpha>> into the equation. \Itsroots are exactly the exponentsof<:imath<x>> that can appear \aslowest exponentsina series solutionofthe differential equation.\ >>)) ; ("majorant series", (<:text<\Aseries <:imath<\sum_{n\geq0} g_n z^n>>withnonnegative coefficients \ is a $(italic"majorant series")ofa series \ <:imath<\sum_{n\geq0} f_n z^n>>withcomplex coefficientsif\ <:imath<|f_n| \leq g_n>>forall <:imath<n>>.\ >>)) ; ("ordinary point", (<:text<\Acomplex number <:imath<z_0>> is an $(italic"ordinary point")ofa \ linear ordinary differential equationwithpolynomial coefficients,if\ the leading coefficientofthe equation does not vanish \ at <:imath<z_0>>.\ >>)) ; ("ramification index", (<:text<\The$(italic"ramification index") is the smallest positive \ integer <:imath<r>> such that the exponentofan exponential factor \ can be expressedasa polynomialin<:imath<x^{-1/r}>>. >>)) ; ("singular point", (<:text<\Acomplex number <:imath<z_0>> is a $(italic"singular point") (or\ $(italic"singularity")ofa linear ordinary differential equation \withpolynomial coefficients,ifthe leading coefficientofthe \ equation vanishes at <:imath<z_0>>.\ >>)) ; ("Laplace transform", (<:text<\The$(italic"Laplace transform")ofafunction<:imath<f>>ofthe \ variable <:imath<z>> is thefunction<:imath<F>> defined by the \ integral <:imath<F(s) = \int_0^\infty e^{-sz} f(z) \,dz>>.\ >>)) ](* A single function, named g for conciseness, as it is called Glossary.g. *)letg ?(display =None) notion =letbody =tryList.assoc notion glossarywith|Not_found-> <:text<($(italic notion) deserves a definition)>>inDC.definition (matchdisplaywith|Somed -> d |None-> notion) bodylettitle _ = <:text<Glossary>>letpar =List.map (fun(_, body) -> <:par< $(t_ent:body) >>) glossary let_serviceGlossary:DC.sec_entities * unitwith{ title = title } = (DC.section (title ()) (ifnot (DynaMoW.Services.Renderings.is_defined ())then<:par<Makesure you have selected a mathematical rendering from theDDMFhome page before looking at the glossary. >>elseDC.unordered_list par), ())

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