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Can Transcendental Functions be Solved Using Polynomial Equations?
- Thread starter profionus
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In summary, the conversation revolves around the topic of solving equations and understanding function tables. Profionus is seeking help with solving equation 30, creating a program to organize results in a chart, and understanding how to read table 1. They also inquire about transcendental functions and the normal method of solving them. Daniel provides an explanation of transcendental functions and suggests ways to approach extrapolating values from a function with two variables.
- #2
- #3
profionus
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function
BTW,
1) what is a transendencal function anyway
2) what is the normal method to solve it
thanks
profionus
BTW,
1) what is a transendencal function anyway
2) what is the normal method to solve it
thanks
profionus
- #4
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There's no equation in #30. It's just the definition of a function. Techincally any non polynomial function is a transcendental one.
Daniel.
Daniel.
- #5
profionus
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Thanks Daniel,
May I know how you read the table 1.
If I had a value B which isn't on the graph, how do I extrapolate for the values of the function G(B,e)
regards,
profionus
May I know how you read the table 1.
If I had a value B which isn't on the graph, how do I extrapolate for the values of the function G(B,e)
regards,
profionus
- #6
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I dunno, it's a lot more difficult, since you got a function of 2 variables, B & xi. Maybe you can fix xi to a certain value (one which is considered in the table) and then try to interpolate for an arbitrary value of B inside the intervals.
Daniel.
About transcendental functions: those polynomial functions must have algebraic numbers as coefficients. Thus, a polynomial function with transcendental coefficients is a transcendental function.
Daniel.
Daniel.
About transcendental functions: those polynomial functions must have algebraic numbers as coefficients. Thus, a polynomial function with transcendental coefficients is a transcendental function.
Daniel.
FAQ: Can Transcendental Functions be Solved Using Polynomial Equations?
What is a transcendental function?
A transcendental function is a mathematical function that cannot be expressed as a finite combination of algebraic functions, such as polynomials, trigonometric functions, and exponential functions. Instead, it involves operations like logarithms, inverse trigonometric functions, and power functions with non-integer exponents.
What is the purpose of transcendental functions?
Transcendental functions are used to model and describe real-world phenomena that cannot be easily expressed using algebraic functions. They are also essential in solving many types of differential equations, which are commonly used in physics, engineering, and other scientific fields.
What are some common examples of transcendental functions?
Some common examples of transcendental functions include the natural logarithm function (ln x), the inverse trigonometric functions (sin⁻¹ x, cos⁻¹ x, tan⁻¹ x), and the exponential function (e^x). Other examples include the hyperbolic functions (sinh x, cosh x, tanh x) and the Bessel functions, which are used to solve differential equations in physics and engineering.
How are transcendental functions different from algebraic functions?
Transcendental functions are different from algebraic functions in that they cannot be expressed using a finite number of algebraic operations. While algebraic functions can be written as a polynomial or a finite combination of basic functions, transcendental functions involve operations that cannot be expressed in this way.
What are some applications of transcendental functions?
Transcendental functions have many applications in fields such as physics, engineering, economics, and statistics. They are used to model and analyze real-world phenomena, solve differential equations, and perform calculations involving complex numbers. They are also essential in the development of mathematical models and algorithms used in various scientific and technological fields.