Table of Integrals: Solving \int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}

  • Context: Graduate 
  • Thread starter Thread starter EngWiPy
  • Start date Start date
  • Tags Tags
    Integrals Table
Click For Summary
SUMMARY

The integral under discussion is defined as \(\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx\), where \(A\), \(B\), and \(C\) are positive integers, and \(K_{(B)}\) represents the B-th order modified Bessel function of the second kind. The forum participants suggest that this integral may be suitable for graduate-level homework help, indicating its complexity and relevance in advanced mathematics. The discussion emphasizes the need for resources such as a table of integrals to find equivalent forms of this expression.

PREREQUISITES
  • Understanding of integral calculus, specifically improper integrals.
  • Familiarity with modified Bessel functions, particularly \(K_{(B)}\).
  • Knowledge of exponential decay functions in integrals.
  • Experience with graduate-level mathematics or physics coursework.
NEXT STEPS
  • Research the properties and applications of modified Bessel functions, focusing on \(K_{(B)}\).
  • Explore tables of integrals, specifically those that include Bessel functions and exponential terms.
  • Study techniques for evaluating improper integrals, particularly those involving polynomial and exponential functions.
  • Learn about graduate-level integral calculus and its applications in physics and engineering.
USEFUL FOR

Graduate students in mathematics or physics, researchers working with advanced integrals, and anyone seeking to understand the application of Bessel functions in integral calculus.

EngWiPy
Messages
1,361
Reaction score
61
Hello,
During my derivation, I am faced with the following integral:

\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx

where A, B, and C are positive integers, K_{(B)} is the B^{th} order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?
 
Physics news on Phys.org
saeddawoud said:
Hello,
During my derivation, I am faced with the following integral:

\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx

where A, B, and C are positive integers, K_{(B)} is the B^{th} order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?

I think this forum is for general discussions rather than homework help, you should post this in homework help section,
here
https://www.physicsforums.com/forumdisplay.php?f=152"
 
Last edited by a moderator:
aaryan0077 said:
I think this forum is for general discussions rather than homework help

Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.
 
CRGreathouse said:
Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.

Okay, whatever you say.
 

Similar threads

Undergrad Solving Stat Mech Integral with Wolfram Alpha
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why does the integral of sine of x^2 from - infinity to + infinity diverge?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Help needed with derivation: solving a complex double integral
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Error propagation of a variable for an integral
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Integral w/ Unknown Table: Solve & Write in Closed-Form
  • · Replies 13 ·
Replies
13
Views
4K
MHB Calculating Integral with Simpson's Rule for Error < $0.5\cdot 10^{-3}$
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Deriving the time-dependent wave equation from Energy eigenfunctions
  • · Replies 1 ·
Replies
1
Views
1K
MHB Polynomial with five roots: determine the roots of the equation x^5+ax^4+bx^3+cx^2+dx+e=0 as functions of a,d and e
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Summing over continuum and uncountable numerocities
  • · Replies 1 ·
Replies
1
Views
3K