International Journal of Mathematics Trends and Technology
Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P541 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P541
In this paper, we obtain the expansions of tan(x) and cot(x) by taking logarithmic derivative of the infinite products for cos(x) and sin(x) respectively. Applying trigonometric identities, series rearrangement technique (for unilateral and bilateral infinite series) and suitable substitutions, we obtain the expansions of cosec(x) and sec(x). We also obtain the expansions, hypergeometric forms, convergence conditions and explicit formulas for m-th derivatives of tan(ax+b), cot(ax+b), cosec(ax+b), sec(ax+b) and related hyperbolic functions.
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M. I. Qureshi, Saurabh Porwal, Dilshad Ahamad, Kaleem A. Quraishi, "Successive differentiations of tangent, cotangent, secant, cosecant functions and related hyperbolic functions (A hypergeometric approach)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 354-367, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P541
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