Ordinary differential equations
Chebyshev's equation is the second order linear differential equation where p is a real (or complex) constant. The equation is named after Russian mathematician Pafnuty Chebyshev. The solutions can be obtained by power series: where the coefficients obey the recurrence relation The series converges for (note, x may be complex), as may be seen by applyingthe ratio test to the recurrence. The recurrence may be started with arbitrary values of a0 and a1,leading to the two-dimensional space of solutions that arises from second orderdifferential equations. The standard choices are: a0 = 1 ; a1 = 0, leading to the solution and a0 = 0 ; a1 = 1, leading to the solution The general solution is any linear combination of these two. When p is a non-negative integer, one or the other of the two functions has its series terminateafter a finite number of terms: F terminates if p is even, and G terminates if p is odd.In this case, that function is a polynomial of degree p and it is proportional to theChebyshev polynomial of the first kind if p is even if p is odd This article incorporates material from Chebyshev equation on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. (Wikipedia).
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
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From playlist Write Linear Equations
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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
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From playlist Bernoulli Differential Equations
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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
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From playlist ⚡️Graph Linear Equations | Learn About
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From playlist Math
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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
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From playlist Mathematics Research Center
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From playlist Differential equations
Summary for graphing an equation in slope intercept form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About