Another Reduction Integration

Real Analysis
Post Reply
jacks
Posts: 102
Joined: Thu Nov 12, 2015 5:26 pm
Location: Himachal Pradesh (INDIA)

Another Reduction Integration

#1

Post by jacks »

If \(\displaystyle y^2 = ax^2+2bx+c\;,\) and \(\displaystyle U_{n} = \int \frac{x^n}{y}dx\;,\) Then prove that \((n+1)\,a\,U_{n}+(2n+1)\,b\,U_{n}+c\,U_{n-1}=x^n\,y\)

and deduce that \(a\,U_{1} = y-b\,U_{0}\) and \(\displaystyle 2a^2U_{2} = y\,(ax-3b)-(ac-3b^2)\,U_{0}\)
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 9 guests