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Why can't some integrals be expressed with elementary equations? For example, why can't the integral of sin(x^2) be equal to some equation rather than a taylor series? Is it because we haven't found a way to integrate it, or do we actually know there isn't a way to solve it using elementary algebra?
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dude "math" lmao
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>>8738266
a taylor series is an equation you NOOB
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>>8738266
The bessel function used to only be able to be expressed in terms of a taylor series until we gave it a name. Thus one just has to wait for the solution to beconr important enough to define a new closed form solution.
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>>8738266
What defines an elementary equation?
Why is sine an elementary equation, but I can't come up with a new one called blab where blab(x) = int sin(x^2)?
So the answer to you is that elementary equations are nothing special, we just assigned special names to them because they pop up a lot in math. There is nothing inherently elementary about them (except for polynomials I guess).
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>>8738266
Look up Differential Galois Theory
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>>8738266
Because you touch yourself at night
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>>8738266
Aside from special values such as x=sqrt pi/2, values of sin(x^2) are also evaluated using methods such as infinite taylor series.
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