Report of the Meetings Volume 3

Report of the Meetings Volume 3

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1834 edition. Excerpt: ...+ r), as long as r is a whole number. The transition from m' and I' (1 + r) when r is a whole number, to m' and I' (1 + r) when r is a general symbol, is made by the principle of the equivalent forms; but by no effort of mind can we connect the first conclusion in each case with the last, without the aid of the intermediate formula, involving symbols which are general in form though specific in value; and in no instance can we interpret the ultimate form, for values of the symbols which are not included in the first, by the aid of the definitions or assumptions which are employed in the establishment of the primary form. In all such cases the interpretation of the ultimate form, when such an interpretation is discoverable, must be governed and determined by a reference to those general properties of it which are independent of the specific values of the symbols.., _, _ _ ' Legendre has named the function 1'(1 + r) = 1. 2... r, the function gamma. Kramp, who has written largely upon its properties, gave it, in his Analyse dcs Refractiorw Astronomigues, the name of faculfe numerique; but in his subsequent memoirs upon it in the earlier volumes of the Armales des Mathematiques of Gergonne he has adopted the name of factorial function, which Arbagost proposed, and which I think it expedient to retain, as recalling to mind the continued product which suggests this creature of algebraical language. and if we possess the law of derivation of M and of M, we d.1' cl.22' can find all the terms of both these series, whatever be the value of r. The first of these terms must be determined through the ordinary definitions of the differential calculus; the second must be determined in form by more

Product details

  • Paperback | 208 pages
  • 189 x 246 x 11mm | 381g
  • United States
  • English
  • black & white illustrations
  • 1236784995
  • 9781236784995