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Jan
21
comment Logarithms of Negative Numbers
$\log z=\log|z|+i\text {Arg} z $ if you take the principal branch. Exponentiating both sides gives $ z=|z|e^{i\text{Arg}( z)} $ as you might hope to expect.
Jan
20
comment Computing the integral of $\int \frac{25x^2}{(x+3)(x-2)^2}\,dx$
what is "impartial differentiation" ?
Jan
20
comment Proof of $\cos(y)$ and $\sin(y)$ using $e^{iy}$
A simple case of substitution followed by simplification will achieve what you want.
Jan
20
revised Solving $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y }=1$
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Jan
20
comment Does $\int_0^\infty \sin(x^{2/3}) dx$ converges?
Maybe $$I=\Im\int_0^\infty e^{ix^{2/3}}dx,$$ and then use the error function. Looks divergent.
Jan
20
revised Closed form for $ \prod_{k=1}^n (a+k^2) $
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Jan
20
revised Closed form for $ \prod_{k=1}^n (a+k^2) $
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Jan
20
answered Closed form for $ \prod_{k=1}^n (a+k^2) $
Jan
20
awarded  Organizer
Jan
20
revised Expansion Of A algebric term
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Jan
20
comment Equation $e^{\frac{1}{x}} - x =0$
Could we use Lagrange inversion theorem here? en.wikipedia.org/wiki/… c.f. also @ PM's comment and @ Lukas' answer.
Jan
20
revised Finding the definite integral of a function that contains an absolute value
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Jan
19
comment Is there a name for functions “opposite in nature” to orthogonal functions?
Thanks David. Are you using the property that the square of a function is always positive here? What if $g_n^2$ is not always positive, e.g. $g_n(x)=\sqrt{h(x)}$ for some $ h $ whose image is $[-a, a] $ ?
Jan
18
revised Is there a name for functions “opposite in nature” to orthogonal functions?
edited tags
Jan
18
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
edited tags
Jan
18
asked Is there a name for functions “opposite in nature” to orthogonal functions?
Jan
17
comment Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
Ah I see. Is this related to the so-called Schmidt process? (related to Gram-Schmidt by any chance...)
Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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