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Sep
15
accepted Inverse Laplace Transform of $(s+1)/z^s$
Sep
15
comment Finding the definite integral of a function that contains an absolute value
No, the modulus is not meaningless for indefinite integrals. When considering definite integrals as your question does we have bounds on the integral, which tells us the domain of the integrand to consider. Because we know the domain, we also know the sign (positive/negative) of a given $x$ value. Hence we can then split the integral into positive/negative parts to evaluate it. Notice also that an indefinite integral can be written as a definite integral since $$\int f(x)dx = \int_\lambda^x f(t)dt,$$ where the "lower bound" $\lambda$ gives a constant of integration.
Sep
15
revised Finding the definite integral of a function that contains an absolute value
added 13 characters in body
Sep
15
comment Finding the definite integral of a function that contains an absolute value
@ surelyyourjoking. Then $x$ would only ever be a positive value (or zero) and so the modulus can be replaced simply by $x$ alone since $∣x∣≥0$ for all $x$.
Sep
15
comment Finding the definite integral of a function that contains an absolute value
@ surelyyourjoking. Then $x$ would only ever be a positive value (or zero) and so the modulus can be replaced simply by $x$ alone since $\mid x\mid\geq 0$ for all $x$.
Sep
15
answered Finding the definite integral of a function that contains an absolute value
Sep
15
comment Range of $\log(16-4x^2-4y^2-z^2)$
Wolfram Alpha: wolframalpha.com/input/…
Sep
14
reviewed Approve suggested edit on Finding Convergeance sum for two power-series.
Sep
14
reviewed Approve suggested edit on Probability of a 75% freethrow shooter making at least 5 shots in a row out of 10.
Sep
12
revised Useful device in complex analysis (Perron's formula)
added 182 characters in body
Sep
12
comment Useful device in complex analysis (Perron's formula)
@ Felix Marin ah yes, I can see that quite clearly now you mention it!
Sep
11
comment Useful device in complex analysis (Perron's formula)
@ robjohn Cool - I did think it was something to do with convergence. Thanks.
Sep
11
comment Useful device in complex analysis (Perron's formula)
@ robjohn why do we "flip the contour to the right" when $a<0$?
Sep
11
comment Useful device in complex analysis (Perron's formula)
Thank you for your answer. I have no particular functions in mind to use, but I can see just how useful it is and wanted to know a bit more about it. Your answer will help me very much. Thanks.
Sep
11
accepted Useful device in complex analysis (Perron's formula)
Sep
11
answered $(1, 1) \cdot (6, 0) = 6?$ Intuition?
Sep
11
comment Can the value of $(-9!)$ be found
@ barak manos It is specific because it is the only one that is concave in the right half of the plane (I think)
Sep
11
comment Can the value of $(-9!)$ be found
There exist other interpolations over $\mathbb{C}$ of the factorial function over $\mathbb{N}_+$, although I've never knowingly seen one. Maybe they are defined at the negative integers.
Sep
11
suggested suggested edit on Find $m_1 , m_2,m_3,m_4\in\mathbb{Q}$ s.t. $\forall a_k,b_k\in\mathbb Z,\,m_1(a_1^2+a_2^2)+m_2(a_3^2+a_4^2)\neq m_3(b_1^2+b_2^2)+m_4(b_3^2+b_4^2)$
Sep
11
revised Useful device in complex analysis (Perron's formula)
added 23 characters in body