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The Fransén–Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis. That is, The Fransén–Robinson constant has numerical value F = 2.8077702420285... (sequence A058655 in the OEIS), with the continued fraction representation [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] (sequence A046943 in the OEIS). Its proximity to Euler's number e = 2.71828... follows from the fact that the integral can be approximated by the standard series for e. The difference is given by

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  • Fransén-Robinson-Konstante
  • Fransén–Robinson constant
  • Constante de Fransén-Robinson
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  • Die Fransén–Robinson-Konstante , benannt nach Arne Fransén und Herman P. Robinson, ist eine mathematische Konstante. Sie ist definiert als die Fläche zwischen dem Kehrwert der Gammafunktion und der x-Achse im Bereich : Die Dezimalentwicklung der Fransén–Robinson-Konstante ist F = 2,80777 02420 28519 36522 50118 65577 72932 30808 59209 30198 … (Folge A058655 in OEIS), ihre Kettenbruchentwicklung [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 10, 1, 4, 7, 2, 2, 2, 46, 18, 1, 1, 3, 1, 1, 4, 5, 1, 1, …] (Folge A046943 in OEIS).
  • La constante de Fransén-Robinson apparait en analyse, dans l'étude de la fonction gamma, définie par : La constante de Fransén-Robinson est alors égale à : Jusqu'à aujourd'hui, on ne sait pas si l'on peut exprimer F à l'aide de sommes, produits ou puissances et de constantes ou fonctions usuelles. La constante de Fransén-Robinson a une valeur numérique F = 2,807… (suite A058655 de l'OEIS), avec une représentation sous forme d'une fraction continue [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] (suite A046943 de l'OEIS).
  • The Fransén–Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis. That is, The Fransén–Robinson constant has numerical value F = 2.8077702420285... (sequence A058655 in the OEIS), with the continued fraction representation [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] (sequence A046943 in the OEIS). Its proximity to Euler's number e = 2.71828... follows from the fact that the integral can be approximated by the standard series for e. The difference is given by
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  • Die Fransén–Robinson-Konstante , benannt nach Arne Fransén und Herman P. Robinson, ist eine mathematische Konstante. Sie ist definiert als die Fläche zwischen dem Kehrwert der Gammafunktion und der x-Achse im Bereich : Die Dezimalentwicklung der Fransén–Robinson-Konstante ist F = 2,80777 02420 28519 36522 50118 65577 72932 30808 59209 30198 … (Folge A058655 in OEIS), ihre Kettenbruchentwicklung [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 10, 1, 4, 7, 2, 2, 2, 46, 18, 1, 1, 3, 1, 1, 4, 5, 1, 1, …] (Folge A046943 in OEIS).
  • La constante de Fransén-Robinson apparait en analyse, dans l'étude de la fonction gamma, définie par : La constante de Fransén-Robinson est alors égale à : Jusqu'à aujourd'hui, on ne sait pas si l'on peut exprimer F à l'aide de sommes, produits ou puissances et de constantes ou fonctions usuelles. La constante de Fransén-Robinson a une valeur numérique F = 2,807… (suite A058655 de l'OEIS), avec une représentation sous forme d'une fraction continue [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] (suite A046943 de l'OEIS).
  • The Fransén–Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis. That is, The Fransén–Robinson constant has numerical value F = 2.8077702420285... (sequence A058655 in the OEIS), with the continued fraction representation [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] (sequence A046943 in the OEIS). Its proximity to Euler's number e = 2.71828... follows from the fact that the integral can be approximated by the standard series for e. The difference is given by and also by The Fransén–Robinson constant can also be expressed using the Mittag-Leffler function as the limit It is however unknown whether F can be expressed in closed form in terms of other known constants. A fair amount of effort has been made to calculate the numerical value of the Fransén–Robinson constant with high accuracy. The value was computed to 36 decimal places by Herman P. Robinson using 11-point Newton–Cotes quadrature, with 65 digits by A. Fransén using Euler–Maclaurin summation, and with 80 digits by Fransén and S. Wrigge using Taylor series and other methods. William A. Johnson computed 300 digits, and Pascal Sebah was able to compute 600 digits using Clenshaw–Curtis integration.
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  • Fransén–Robinson Constant
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  • Fransen-RobinsonConstant
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