Find the generating function F1 of the canonical transformation P=ln sin (p/q) and Q=q cot p
Added by Tammy P.
Step 1
The transformation equations involve both old and new momenta (p and P), and old and new coordinates (q and Q). Therefore, the generating function should be of the type F1(q,Q) or F2(p,P). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 54 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Generating function for Hermite polynomials A generating function ̐(x,t) for a family of functions [such as the Hermite polynomials] is defined by its Taylor series in t, ̐(x,t) = ∑_{n=0}^{∑} rac{H_n(x)}{n!} t^n, where the coefficients are given by the functions in question --- in our problem, by the Hermite polynomials. Using the Rodrigues formula, H_n(x) = (-1)^n e^{x^2} rac{d^n e^{-x^2}}{dx^n} and the fact that rac{∂}{∂t} e^{(t-x)^2} = -rac{∂}{∂x} e^{(t-x)^2} show that ̐(x,t) = e^{2tx-t^2}
Sri K.
David N.
Differentiate the moment-generating function in Exercise 3.147 to find $E(Y)$ and $E\left(Y^{2}\right) .$ Then find $V(Y)$.
Discrete Random Variables and Their Probability Distributions
Moments and Moment-Generating Functions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD