Sometimes simple arithmetic operations containing hyperbolic functions can automatically produce other hyperbolic functions. Simplification of simple expressions containing hyperbolic functions In cases where the argument has the structure or, e or with integer, trigonometric functions can be automatically transformed into other trigonometric or hyperbolic functions. Mathematica also automatically simplifies the composition of the direct and any of the inverse hyperbolic functions into algebraic functions of the argument. Mathematica automatically simplifies the composition of the direct and the inverse hyperbolic functions into the argument. Mathematica uses symmetries and periodicities of all the hyperbolic functions to simplify expressions. The remaining digits are suppressed, but can be displayed using the function InputForm. In this case, only six digits after the decimal point are shown in the results. Mathematica always evaluates mathematical functions with machine precision, if the arguments are machine numbers. Here are 50‐digit approximations to the six hyperbolic functions at the complex argument.
The next input calculates 10000 digits for, ,, ,, and and analyzes the frequency of the occurrence of the digit in the resulting decimal number. Within a second, it is possible to calculate thousands of digits for the hyperbolic functions. The next inputs calculate 100‐digit approximations of the six hyperbolic functions at. įor a generic machine‐number argument (a numerical argument with a decimal point and not too many digits), a machine number is returned. For instance, for the argument, the Sinh function evaluates to. Here are three examples: CForm, TeXForm, and FortranForm.Īutomatic evaluations and transformationsĮvaluation for exact, machine-number, and high-precision argumentsįor a simple exact argument, Mathematica returns an exact result. Mathematica also knows the most popular forms of notations for the hyperbolic functions that are used in other programming languages. Here is a list hypFunctions of the six trigonometric functions in TraditionalForm. Here is a list hypFunctions of the six hyperbolic functions in StandardForm. Following Mathematica's general naming convention, the StandardForm function names are simply capitalized versions of the traditional mathematics names. These involve numeric and symbolic calculations and plots.Īll six hyperbolic functions are represented as built‐in functions in Mathematica. Examples of evaluating Mathematica functions applied to various numeric and exact expressions that involve the hyperbolic functions or return them are shown. The following shows how the six hyperbolic functions are realized in Mathematica. Introduction to the Hyperbolic Functions in Mathematica
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