| I. ARITHMETICAL PROGRESSION II. GEOMETRICAL PROGRESSION III. ARITHMETICAL AND GEOMETRICAL PROGRESSION IV. POWERS OF NATURAL NUMBERS V. PRODUCTS OF NATURAL NUMBERS VI. FIGURATE AND POLYGONAL NUMBERS VII. INVERSE NATURAL NUMBERS Vlll. EXPONENTIAL AND LOGARITHMIC SERIES IX. BINOMIALS X. SIMPLE INVERSE PRODUCTS XI. OTHER INVERSE PRODUCTS XII. SIMPLE FACTORIALS xIII. OTHER POWER SERIES (Bernoulli's and Euler's numbers) IV. TRIGONOMETRICAL SUMMATIONS XV. HYPERBOLIC SUMMATIONS XVI. TRIGONOMETRICAL EXPANSIONS XVll. HYPERBOLIC EXPANSIONS XVIII. TAYLOR'S AND MACLAURIN'S THEOREM XlX. BESSEL FUNCTIONS XX. ELLIPTIC FUNCTIONS. XXI. VARIOUS INTEGRALS. XXII. BETA AND GAMMA FUNCTIONS XXIlI. INFINITE PRODUCTS XXIV. FOURIER'S SERIES XXV. HYPERGEOMETRIC FUNCTIONS XXVI. RELATIONS BETWEEN PRODUCTS AND SERIES XXVII. SPECIAL FUNCTIONS XXVIII. ZETA FUNCTIONS XXIX. LEGENDRE POLYNOMIALS XXX. SPECIAL PRODUCTS XXXI. GENERAL FORMS XXXII. DOUBLE AND TREBLE SERIES XXXIlI. BERNOULLI'S FUNCTIONS Bernoulli's Numbers Table of Bernoulli's Numbers in Vulgar Fractions Table of Bernoulli's Numbers in Integers and Repeating Decimals Values of Constants in Series (305) to (318) and (1130) Euler's Numbers Euler's Constant Sum of Power Series Relations between Bernoulli's N umbers |
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