Tables of the Exponential Function and of the Circular Sine and Cosine to Radian Argument (Memoirs of the National Academy of Sciences) (Volume 14) Book PDF, ePub eBook

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Book Descriptions:
The tables accompanying this paper have been prepared with the expectation of meeting a twofold requirement. The first was to obtain a few high place values at sufficiently small intervals of argument for general use in the evaluation of integrals and other functions; the other object was to obtain a basis for subsequent interpolation to small intervals of argument for use in the construction of complete 10-place tables which are applicable in the various fields of pure and applied mathematics. The need of tables meeting these and other requirements has been emphasized by various authors.

The most important tables of extended values of the exponential function in which the exponents are integers or fractions have been constructed by Schulze, Bretschneider, Newman, Gram, Glaisher, and Burgess. Bretschneider included a few high place values of the circular sine and cosine to radian argument, but with the exception of these and a few values computed by Gudermann, there appears to be no extended values of these important functions.

Schulze gives values of the ascending exponential at intervals of unity between the limits 1 and 24, inclusive, to 28 or 29 significant figures, and for the special arguments 25, 30, and 60 his values include 32 or 33 figures. In so far as I have been able to ascertain, Schulze gives no information regarding methods of computation or accuracy of results. Glaisher verified the first 15 figures of Schulze's value of e¹⁶ by direct substitution in the series; the first 13 powers of e were verified to 22 places of decimals; and the values of e¹⁴, e¹⁵, ... e²⁵ to 15 places of decimals by means of the relation...

Tables of the Exponential Function and of the Circular Sine and Cosine to Radian Argument (Memoirs of the National Academy of Sciences) (Volume 14) by C. E. van Orstrand

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