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FORMULAS FOR POWERS OF THE HYPERBOLIC TANGENT WITH AN APPLICATION TO HIGHER-ORDER TANGENT NUMBERS

LOMONT, J.S.

The Rocky Mountain journal of mathematics, 2005-01, Vol.35 (4), p.1217-1231 [Periódico revisado por pares]

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Título:
FORMULAS FOR POWERS OF THE HYPERBOLIC TANGENT WITH AN APPLICATION TO HIGHER-ORDER TANGENT NUMBERS
Autor: LOMONT, J.S.
Assuntos: Coefficients ; Integers ; Maclaurin series ; Numbers ; Polynomials ; Tangents
É parte de: The Rocky Mountain journal of mathematics, 2005-01, Vol.35 (4), p.1217-1231
Descrição: It is shown that the function tanh2n+1(x) is a linear combination of even-order derivatives of tanh(x), while the function 1 — tanh2n+2(x) is a linear combination of odd-order derivatives of tanh(x). These results are then used to express higher-order tangent numbers (coefficients in the Maclaurin series for tanhn(x)) as linear combinations of the ordinary tangent numbers (coefficients in the Maclaurin series for tanh(x)).
Editor: The Rocky Mountain Mathematics Consortium
Idioma: Inglês

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