Showing papers on "Inverse trigonometric functions published in 1973"
Book•
01 Jan 1973
TL;DR: Inverse Laplace Transforms and Inverse Trigonometric Functions as mentioned in this paper have also been used to generate generalized hypergeometric functions, such as the generalized generalized Hypergeometric function (GHEF).
Abstract: I. Laplace Transforms.- 1.1 General Formulas.- 1.2 Algebraic Functions.- 1.3 Powers of Arbitrary Order.- 1.4 Sectionally Rational- and Rows of Delta Functions.- 1.5 Exponential Functions.- 1.6 Logarithmic Functions.- 1.7 Trigonometric Functions.- 1.8 Inverse Trigonometric Functions.- 1.9 Hyperbolic Functions.- 1.10 Inverse Hyperbolic Functions.- 1.11 Orthogonal Polynomials.- 1.12 Legendre Functions.- 1.13Bessel Functions of Order Zero and Unity.- 1.14 Bessel Functions.- 1.15 Modified Bessel Functions.- 1.16 Functions Related to Bessel Functions and Kelvin Functions.- 1.17 Whittaker Functions and Special Cases.- 1.18 Elliptic Functions.- 1.19 Gauss' Hypergeometric Function.- 1.20 Miscellaneous Functions.- 1.21 Generalized Hypergeometric Functions.- II. Inverse Laplace Transforms.- 2.1 General Formulas.- 2.2 Rational Functions.- 2.3 Irrational Algebraic Functions.- 2.4 Powers of Arbitrary Order.- 2.5 Exponential Functions.- 2.6 Logarithmic Functions.- 2.7 Trigonometric- and Inverse Functions.- 2.8 Hyperbolic- and Inverse Functions.- 2.9 Orthogonal Polynomials.- 2.10 Gamma Function and Related Functions.- 2.11 Legendre Functions.- 2.12 Bessel Functions.- 2.13 Modified Bessel Functions.- 2.14 Functions Related to Bessel Functions and Kelvin Functions.- 2.15 Special Cases of Whittaker Functions.- 2.16 Parabolic Cylinder Functions and Whittaker Functions.- 2.17 Elliptic Integrals and Elliptic Functions.- 2.18 Gauss' Hypergeometric Functions.- 2.19 Generalized Hypergeometric Functions.- 2.20 Miscellaneous Functions.
577 citations
TL;DR: In this paper, a brief account of the results on multiple trigonometric and orthogonal series that have been obtained so far and are fundamental from our point of view is given.
Abstract: In this article we give a brief account of the results on multiple trigonometric and orthogonal series that have been obtained so far and are fundamental from our point of view. We also state results on simple trigonometric and orthogonal series that are new or have been obtained recently.
39 citations
TL;DR: For a nonconstant L 2 (−π, π) function f, this paper proved that the inequalities are sharp and showed that for a non-constant function f, they are sharp.
Abstract: For a nonconstant L2 (−π, π) function f, we prove that and that the inequalities are sharp.
3 citations
08 May 1973
TL;DR: Algorithms for the automatic evaluation of elementary functions were studied to determine their suitability for hardware implementation, in terms of their accuracy, convergence rate, and hardware requirements.
Abstract: : Algorithms for the automatic evaluation of elementary functions were studied. Available algorithms obtained from current literature were analyzed to determine their suitability for hardware implementation, in terms of their accuracy, convergence rate, and hardware requirements. The functions considered were quotient, arctangent, cosine/sine, exponential, power function, logarithm, tangent, square root, and product. (Author)
3 citations
1 citations
1 citations