Selected Topics in the Theory of Divergent Series And of Continued Fractions
Selected Topics in the Theory of Divergent Series And of Continued Fractions
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See 546 ; also No. 66a for work on differential equations of the 1st order.
B. Miscellaneous Differential Equations of the Second Order.
In a numerous class of continued fractions the denominators of the convergents satisfy allied (Heun, " gleichgruppige ") differ ential equations of the second order. Early instances are found in works of Gauss (No. 114), Jacobi (No. 65) and Heine (No. 72). The theory, from two different aspects, is furthest developed in 66a and 76.
178 THE BOSTON COLLOQUIUM.
6...5. Jacobi. Untersuchung iiber die Differentialgleichung der hyper- geometrischen Reihe. Nachlass. Jour, fur Math. , vol. 56, 1859 ; see in particular 8, pp. 160-161, or Werke, vol. 6, p. 184.
66. Laguerre. (a) Sur la reduction en fractions continues d une frac tion qui satisfait a une equation differentielle lineaire du pre mier ordre dont les coefficients sont rationnels. Jour, de Math. , ser. 4, vol. 1, pp. 135-165, 1885. (jt**^ V*l y. ^\^5 (This is a comprehensive memoir which incorporates substan tially all the following memoirs : (b) Sur la reduction en fractions continues d une classe assez >> 6tendue de fonctions.
What to read after Selected Topics in the Theory of Divergent Series And of Continued Fractions?
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To quickly assess the difficulty of the text, read a short excerpt:
See 546 ; also No. 66a for work on differential equations of the 1st order.
B. Miscellaneous Differential Equations of the Second Order.
In a numerous class of continued fractions the denominators of the convergents satisfy allied (Heun, " gleichgruppige ") differ ential equations of the second order. Early instances are found in works of Gauss (No. 114), Jacobi (No. 65) and Heine (No. 72). The theory, from two different aspects, is furthest developed in 66a and 76.
178 THE BOSTON COLLOQUIUM.
6...5. Jacobi. Untersuchung iiber die Differentialgleichung der hyper- geometrischen Reihe. Nachlass. Jour, fur Math. , vol. 56, 1859 ; see in particular 8, pp. 160-161, or Werke, vol. 6, p. 184.
66. Laguerre. (a) Sur la reduction en fractions continues d une frac tion qui satisfait a une equation differentielle lineaire du pre mier ordre dont les coefficients sont rationnels. Jour, de Math. , ser. 4, vol. 1, pp. 135-165, 1885. (jt**^ V*l y. ^\^5 (This is a comprehensive memoir which incorporates substan tially all the following memoirs : (b) Sur la reduction en fractions continues d une classe assez >> 6tendue de fonctions.
What to read after Selected Topics in the Theory of Divergent Series And of Continued Fractions?
You can find similar books in the "Read Also" column, or choose other free books by Edward Burr Van Vleck to read onlineMoreLess
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