a. and sb. [f. prec. + -(I)AL.] A. adj.
1. That has the function of setting forth or exhibiting. rare.
1730–6. in Bailey (folio).
1809–10. Coleridge, Friend (1818), III. 185. Where the hypothesis is an exponential image … of an idea.
2. Math. Involving the unknown quantity or variable as an exponent, or as part of an exponent. So exponential equation, function, quantity, etc.
Exponential curve, one expressed by an exponential equation. † E. calculus: see quot. 1796. E. series, the infinite series 1+x+1/2x2+1/6x3 etc.; E. theorem, the theorem that the value of ex (the ‘exponential,’ or Napierian antilogarithm, of x) is expressed by this series.
1704. J. Harris, Lex. Techn., II. s.v., Exponential curves are such as partake both of the nature of Algebraick and Transcendent ones.
1715. Phil. Trans., XXIX. 212. These Equations he now calls Exponential.
1739. Anderson, in Rigaud, Corr. Sci. Men (1841), I. 342. The exponential equation xx=d.
1784. Phil. Trans., LXXIV. 401. P is either an algebraical, exponential, or fluential fluxion of X.
1796. Hutton, Math. Dict., Exponential Calculus, the method of differencing, or finding the fluxions of Exponential quantities, and of summing up those differences, or finding their fluents.
1881. Maxwell, Electr. & Magn., I. 221. We call the exponential quantity … the hyperbolic cosine of β.
B. sb. Math. An exponential quantity or function; spec. the Napierian base e raised to the power denoted by the variable; the Napierian antilogarithm of the variable.
1784. Waring, in Phil. Trans., LXXIV. 395. When the terms are exponentials of superior orders.
1833. Sir W. R. Hamilton, in R. P. Graves, Life, II. 58. My extension of Herschel’s theorem for the development of functions of exponentials.
1885. Athenæum, 11 July, 52/1. The discussion of logarithms and exponentials by means of the properties of the logarithmic spiral.
