Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions

• Autores: Yogesh J. Bagul, Christophe Chesneau
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 21, Nº. 1, 2019, págs. 21-35
• Idioma: inglés
• DOI: 10.4067/S0719-06462019000100021
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen El objetivo principal de este artículo es establecer cotas inferiores y superiores precisas para funciones útiles tales como las funciones exponenciales, con énfasis especial en exp(−x²), las funciones trigonométricas (coseno y seno) y las funciones hiperbólicas (coseno y seno). Las cotas obtenidas para el coseno hiperbólico son muy precisas. Se presentan, tanto nuevas demostraciones y refinamientos, como resultados nuevos. Algunos resultados numéricos y gráficos ilustran los resultados encontrados.

  • English

    Abstract The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x²), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.

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