Stating the Gil-Pelaez Theorem in terms of a real integral
In (Gil-Pelaez, 1951), the following is stated $F(x)= \frac{1}{2}+\frac{1}{2\pi}\int_0^\infty\frac{e^{itx}\phi(-t)-e^{-itx}\phi(t)}{it}dt.$ I am trying to...
19 Apr 2026 1 READS
Archive: News
What is the equation used to calculate a linear trendline?
What are the equations to calculate a linear trendline over a set of points? EDIT: "In excel it is done automatically but how to manually calculate a line...
19 Apr 2026 1 READS
![Software for 3D graphing complex functions? [closed]](https://edu.smbbmcl.edu.pk/uploads/software-for-3d-graphing-complex-functions-closed_720.jpg)
Software for 3D graphing complex functions? [closed]
(I am new to this forum.) I am interesting in seeing what some equations look like when they are plotted 3-dimentionally, with one axis real numbers, the ...
19 Apr 2026 1 READS
What does the notation min max mean?
Min clearly means minimum and max maximum, but I am confused about a question that says "With $x, y, z$ being positive numbers, let $xyz=1$, use the AM-GM...
19 Apr 2026 1 READS
dot product between vector and matrix
In my book on fluid mechanics there is an expression $$ \boldsymbol{\nabla}\cdot \boldsymbol{\tau}_{ij} $$ where $\boldsymbol{\tau}_{ij}$ is a rank-2 tens...
19 Apr 2026 1 READS
Finding the perimeter of a parallelogram.
ABCD is a parallellogram in which $$\angle D = 120^\circ .$$ The bisector of angle D bisects the side AB. If the length of the bisector is 5 cm, then what...
19 Apr 2026 1 READS
How can I prove that the Core of $H$ in $G$ is a normal subgroup?
Given $G$ a group and $H$ a subgroup of $G$, how can I prove that ${\rm Core}_H G:=\bigcap_{g\in G} gHg^{-1}$ is a normal subgroup of $G$? I've prove...
19 Apr 2026 1 READS
How to find coordinates of 3rd vertex of a right angled triangle when everything else is known?
I want to locate precisely the 3rd coordinate of a right angled triangle. I have: the length of three sides The three angles The other two coordinates of ...
19 Apr 2026 1 READS
What is the Fisher information of a sequence of independent Poisson random variables?
$X_1,...,X_n$ are independent Poisson random variables with$ X_j $having parameter$j\lambda$.What is the fisher information contained in $(X_1,...,X_n)$ a...
19 Apr 2026 1 READS
Double u-substitution Problem
I have to find $$\int\limits_{0}^{1}x(x+a)^{1/p}\text{ d}x$$ and I'm told to use two substitutions, $u=(x+a)^{1/p}$ and $u=x+a$. However, I can'...
19 Apr 2026 1 READS
