Derivatives of the Trigonometric Functions

2015 ◽  
pp. 238-273
Keyword(s):  
Trigonometric Functions ◽  
Derivatives Of

scholarly journals Approximations of the Sixth Order with the Polynomial and Non-polynomial Splines and Variational-difference Method

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Sixth Order ◽  
Trigonometric Functions ◽  
Polynomial Splines ◽  
Local Basis ◽  
Polynomial Approximations ◽  
Approximation Theorems ◽  
Second Derivatives ◽  
Variational Difference Method ◽  
Grid Nodes ◽  
Derivatives Of

This paper discusses the approximations with the local basis of the second level and the sixth order. We call it the approximation of the second level because in addition to the function values in the grid nodes it uses the values of the function, and the first and the second derivatives of the function. Here the polynomial approximations and the non-polynomial approximations of a special form are discussed. The non-polynomial approximation has the properties of polynomial and trigonometric functions. The approximations are twice continuously differentiable. Approximation theorems are given. These approximations use the values of the function at the nodes, the values of the first and the second derivatives of the function at the nodes, and the local basis splines. These basis splines are used for constructing variational-difference schemes for solving boundary value problems for differential equations. Numerical examples are given

scholarly journals Repeated Derivatives of Hyperbolic Trigonometric Functions and Associated Polynomials

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 138 ◽  
Author(s):  
Giuseppe Dattoli ◽  
Silvia Licciardi ◽  
Rosa Maria Pidatella ◽  
Elio Sabia
Keyword(s):  
Point Of View ◽  
Combinatorial Analysis ◽  
Trigonometric Functions ◽  
Special Polynomials ◽  
Associated Polynomials ◽  
Derivatives Of

Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by other authors and develop a complementary point of view for the repeated derivatives of sec ( . ) , tan ( . ) and for their hyperbolic counterparts.

Derivatives of Trigonometric Functions-Revisited

1975 ◽  
Vol 68 (7) ◽  
pp. 572-573
Author(s):  
R. S. Luthar
Keyword(s):  
Trigonometric Functions ◽  
Derivatives Of

Here's a classic topic from analysis treated in an interesting new way with skillful application of identities and differentiation techniques.

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