Im trying to find the Fourier transform of the function: $$\frac{t}{\left(t^2+a^2\right)^{\frac{3}{2}}};$$ As well the Fourier transform of the function: $$\frac{1}{\left(t^2+a^2\right)^{\frac{3}{2}}}.$$ It looks very similar to the first modified Bessel function but not quite, I wondered if there is an analytic expression for that transformation.
2026-03-29 07:30:34.1774769434
Fourier transform of $\frac{t}{(a^2+t^2)^{3/2}}$.
72 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in FOURIER-TRANSFORM
- Proof of Fourier transform of cos$2\pi ft$
- Find the convergence of series of a sequence of functions in $L^2(\mathbb{R})$
- solving a simple ODE with Fourier transform
- How can we prove that $e^{-jωn}$ converges at $0$ while n -> infinity?
- Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $
- Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform
- Arcsin of a number greater than one
- Complex numbers in programming
- Power spectrum of field over an arbitrarily-shaped country
- Computing an inverse Fourier Transform / Solving the free particle Schrödinger equation with a gaussian wave packet as initial condition
Related Questions in BESSEL-FUNCTIONS
- How to prove $\int_{0}^{\infty} \sqrt{x} J_{0}(x)dx = \sqrt{2} \frac{\Gamma(3/4)}{\Gamma(1/4)}$
- What can be said about the series $\sum_{n=1}^{\infty} \left[ \frac{1}{n} - \frac{1}{\sqrt{ n^2 + x^2 }} \right]$
- A closed-form of an integral containing Bessel's function
- Sources for specific identities of spherical Bessel functions and spherical harmonics
- The solution to the integral $\int_{0}^{\infty} \log(x) K_{0}(2\sqrt{x})\,dx$
- Laplace transform of $t^\mu I_\nu(at)$
- Integral of product of Bessel functions of first kind and different order and argument
- Series involving zeros of Bessel functions
- Finding the kernel of a linear map gotten from a linear map with one kind of bessel function $j_i$ and replacing them with the $y_j$
- Transcendental equation with Bessel function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?