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calcul des residus et ses applications à la théorie des fonctions

calcul des residus et ses applications à la théorie des fonctions

          
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About the Book

Les progrès réalisés depuis quelques années dans la théorie des fonctions analytiques ont fait ressortir combien sont toujours fécondes et efficaces les méthodes ingénieuses créées par Cauchy, parmi lesquelles il convient de citer en premier lieu le Calcul des résidus. Il n'est donc pas sans intérêt de revenir maintenant sur ce Calcul classique et d'étudier systématiquement le rôle qu'il joue dans la théorie des fonctions proprement dite. C'est ce que nous avons tâché de faire dans ce petit Livre, en vue de faciliter dans une certaine mesure l'accès des parties modernes de l'Analyse. Dans le premier Chapitre, nous passons rapidement en revue les principes et théorèmes généraux dont nous aurons à faire usage, en cherchant d'ailleurs à varier un peu ce sujet tant de fois exposé. Le deuxième Chapitre contient diverses applications du Calcul des résidus, dues pour la plupart à Cauchy. Cependant les limites restreintes imposées à cet Ouvrage ne nous ont permis de donner qu'une idée très imparfaite du parti que Cauchy avait tiré lui-même de son Calcul. Parmi les applications faites par lui qui n'ont pu trouver place dans ce Chapitre, nous devons signaler surtout la méthode qu'il a employée pour obtenir des séries analogues à celle de Fourier, méthode dont on trouve une très belle exposition au Tome II du Traité d'Analyse de M. Picard. Le troisième Chapitre est consacré aux formules sommatoires. Le Calcul des résidus, appliqué systématiquement, permet de rattacher toutes ces formules, avec leurs conséquences multiples, à un même principe simple et naturel, et contribue ainsi à mettre plus d'ordre et d'unité dans cette partie si intéressante de l'Analyse. Comme application de ces formules, nous en déduisons, au quatrième Chapitre, une grande partie des expressions et des développements trouvés, à différentes époques et par différentes méthodes, pour la fonction gamma et pour la fonction de Riemann. Ce Chapitre contient aussi quelques résultats nouveaux relatifs à la série


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Product Details
  • ISBN-13: 9791041940226
  • Publisher: Bod Third Party Titles
  • Publisher Imprint: Culturea
  • Height: 210 mm
  • No of Pages: 144
  • Spine Width: 9 mm
  • Width: 148 mm
  • ISBN-10: 104194022X
  • Publisher Date: 14 Dec 2022
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Weight: 199 gr


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