In mathematics before the 1970s, the term umbral calculus was understood to mean the surprising similarities between otherwise unrelated polynomial equations, and certain shadowy techniques that can be used to 'prove' them. These techniques were introduced by John Blissard in 1861 and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas, who used the technique extensively.

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  • In mathematics before the 1970s, the term umbral calculus was understood to mean the surprising similarities between otherwise unrelated polynomial equations, and certain shadowy techniques that can be used to 'prove' them. These techniques were introduced by John Blissard in 1861 and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas, who used the technique extensively. In the 1930s and 1940s, Eric Temple Bell attempted to set the umbral calculus on a rigorous footing, perhaps not altogether successfully. In the 1970s, Steven Roman, Gian-Carlo Rota, and others developed the umbral calculus by means of linear functionals on spaces of polynomials. Currently, umbral calculus is understood primarily to mean the study of Sheffer sequences, including polynomial sequences of binomial type and Appell sequences.
  • En mathématiques, avant les années 1970, le terme calcul symbolique (en anglais, "umbral calculus", ce qui se traduit par "calcul obscur") était compris comme signifiant les similarités surprenantes entre des équations polynômiales non reliées entre elles, et certaines techniques obscures qui peuvent être utilisées pour les 'démontrer'. Ces techniques furent introduites au cours du XIX siècle et sont quelquefois appelées la méthode symbolique de Blissard, et sont quelquefois attribuées à James Joseph Sylvester, qui utilisa la technique de manière extensive, ou au mathématicien Edouard Lucas. Dans les années 1930 et 1940, Eric Temple Bell essaya de fixer des bases rigoureuses au calcul symbolique, peut-être pas tout à fait avec succès. Dans les années 1970, Steven Roman, Gian-Carlo Rota et d'autres développèrent le calcul symbolique du point de vue des formes linéaires sur les espaces de polynômes. Actuellement, le calcul symbolique est compris de prime abord au sens d'étude des suites de Sheffer, incluant les suites de polynômes de type binômiaux et les suites d'Appell.
  • In matematica, prima degli anni 1970, con il termine calcolo umbrale si indicavano le sorprendenti somiglianze tra molte equazioni polinomiali allora prive di collegamenti logici, nonché certe tecniche poco giustificate che potevano essere usate per 'dimostrare' tali equazioni. Queste tecniche erano state introdotte nel XIX secolo e da taluni sono state chiamate metodo simbolico di Blissard, da altri sono state attribuite a James Joseph Sylvester (che le ha utilizzate ampiamente) e da altri ancora a Edouard Lucas. Negli anni 1930 e 1940 Eric Temple Bell ha cercato di fornire il calcolo umbrale di fondamenti rigorosi, riuscendoci solo in parte. Negli anni 1970 Gian-Carlo Rota, Steven Roman e altri sono riusciti a sviluppare il calcolo umbrale sulla solida base dei funzionali lineari sugli spazi di polinomi. Attualmente il calcolo umbrale viene considerato primariamente uno strumento per lo studio delle sequenze di Sheffer, e in particolare delle sequenze polinomiali di tipo binomiale e delle sequenze di Appell.
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  • Umbral Calculus
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  • UmbralCalculus
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  • In mathematics before the 1970s, the term umbral calculus was understood to mean the surprising similarities between otherwise unrelated polynomial equations, and certain shadowy techniques that can be used to 'prove' them. These techniques were introduced by John Blissard in 1861 and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas, who used the technique extensively.
  • En mathématiques, avant les années 1970, le terme calcul symbolique (en anglais, "umbral calculus", ce qui se traduit par "calcul obscur") était compris comme signifiant les similarités surprenantes entre des équations polynômiales non reliées entre elles, et certaines techniques obscures qui peuvent être utilisées pour les 'démontrer'.
  • In matematica, prima degli anni 1970, con il termine calcolo umbrale si indicavano le sorprendenti somiglianze tra molte equazioni polinomiali allora prive di collegamenti logici, nonché certe tecniche poco giustificate che potevano essere usate per 'dimostrare' tali equazioni.
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  • Umbral calculus
  • Calcul symbolique
  • Calcolo umbrale
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