4:20 AM
Feb 19 at 9:11, by Martin Sleziak
Feb 20 at 13:05, by Martin Sleziak
The tag is back. And the tag was created in the same question.
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Appell's two-variable functions $F_1, F_2, F_3$ and $F_4$ are known to have numerous uses in applied mathematics, notably mathematical Physics. I am looking for generalized Laplace transforms (if they exist) of these functions relative to one of the two variables (I found at least two references ...

In mathematics, Appell series are a set of four hypergeometric series F1, F2, F3, F4 of two variables that were introduced by Paul Appell (1880) and that generalize Gauss's hypergeometric series 2F1 of one variable. Appell established the set of partial differential equations of which these functions are solutions, and found various reduction formulas and expressions of these series in terms of hypergeometric series of one variable. == Definitions == The Appell series F1 is defined for |x| < 1, |y| < 1 by the double series F 1...
A new tag . It has a tag-excerpt: "For questions related to many-sorted logic, languages, and structures."
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I was reading about Many-sorted logic and I kept seeing a lot of authors claiming that "When there are only finitely many sorts in a theory, many-sorted first-order logic can be reduced to single-sorted first-order logic". I get that this is done by introducing, for every sort $a$, a unary predic...

Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive "parts of speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be done only accordingly, respecting the "sorts". There are various ways to formalize the intention mentioned above; a many-sorted logic is any package of information which fulfils it. In most cases, the following...
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Here is something I've found on the internet \begin{aligned} f-\int f&=1\\ \left(1-\int\right)f&=1\\ f&=\left(\frac1{1-\int}\right)1\\ &=\left(1+\int+\int\int+\dots\right)1\\ &=1+\int1+\int\int1+\dots\\ &= 1+x+\frac{x^2}2+\dots\\ &= e^x \end{aligned} At first I interpreted this as a joke, but...

Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. == History == The idea of representing the processes of calculus, differentiation and integration, as operators has a long history that goes back to Gottfried Wilhelm Leibniz. The mathematician Louis François Antoine Arbogast was one of the first to manipulate these symbols independently of the function to which they were applied.This approach was further developed...

8 hours later…
11:56 AM
And the tag is back.
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Consider a $2 \times 4$ matrix $A = \begin{bmatrix} a_1 & b_1 & c_1 & d_1 \\ a_2 & b_2 & c_2 & d_2 \\ \end{bmatrix}$. Its all minors of order 2, such as $A_{13} = \begin{vmatrix} a_1 & c_1 \\ a_2 & c_2 \\ \end{vmatrix}$ representing the minor formed by selecting the first and third columns, satis...

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The functional equation identity, (assuming also $\,f(-x)=-f(x)\,$ for all $\,x$), $$f(a)f(b)f(a\!-\!b) + f(b)f(c)f(b\!-\!c) + f(c)f(a)f(c\!-\!a) + f(a\!-\!b)f(b\!-\!c)f(c\!-\!a) = 0 \tag{1}$$ for all $\,a,b,c\,$ has solutions $f(x)=k_1\sin(k_2\,x)$ and $f(x)=k_1\tan(k_2\,x)\,$ with \$\,k_1,k_...

2 hours later…

2 hours later…
3:10 PM
You have already been asked not to add a new tag to posts without first going through the process on Meta. Right now, the voting on meta indicates that the community does not feel a need for this tag (though you have only given it two days). At this point, the creation of a new tag does not seem warranted. — Xander Henderson ♦ 3 hours ago
@XanderHenderson Okay, I jumped the gun a bit. I apologize again for my inexperience. — Somos 3 hours ago