AN ACCELERATION OF CONVERGENCE TO SOME GENERALIZED-EULER-CONSTANT FUNCTION

作者：Lampret V^*

来源：Miscolc Mathematical Notes, 2013, 14(3): 991-996.

DOI：10.18514/mmn.2013.548

• acceleration of convergence
• generalized Euler%26apos
• s constant
• generalized
• gamma-sequence

For the generalized- Euler- constant function gamma. a/, %26lt;br%26gt;gamma. a/ W D lim n ! 1 0 @ n 1 X k D 0 1 a C k ln a C n 1 a 1 A. a %26gt; 0/; %26lt;br%26gt;and for any positive integer q gamma 2, using the Bernoulli numbers B 2 m, the sequences n 7 ! A n. a; q/, n 7 ! B n. a; q/ and n 7 ! C n. a; q/, having the properties %26lt;br%26gt;lim n ! 1 n 2 q 2 gamma. a/ A n. a; q/ gamma D B 2 q 2 2q 2; lim n ! 1 n 2 q 2 gamma. a/ B n. a; q/ gamma D gamma 1 2 3 2 q gamma B 2 q 2 2q 2 %26lt;br%26gt;and lim n 1 n 2 q 1 gamma. a/ C n. a; q/ gamma D 1 2 B 2 q 2; %26lt;br%26gt;are determined.

• 出版日期2013