Question
Show that P1(x) is orthogonal to [Pn(x)]2 on the interval (-1, 1).
Answer :
Word Count : 199
________ ______ ___ _____ ______ ______ ___ _____ _____.
______ _________ __________ ___ _____ _________ ______ ____.
_________ ______ ___ ______ ______ __________.
________ ___ __________ ____ ______.
_____ _________ __________ _______ ___ __________ _____.
_________ ________ __________ _______ ________.
______ _______ ___ _______ ______.
___ __________ __________ ____ _____ __________ __________ ______.
__________ __________ __________ ____ __________ ______.
______ _____ ___ _____ _____ _______ ________ ____ ___ ______.
________ __________ ____ ______ ____ ___ __________.
__________ __________ ____ ______ __________ __________ _____ _____ _______ __________ ____ _________.
___ _______ __________ _________ _____ ___ _________ ____ ____ ____.
______ _______ __________ _________ ___ ____ ______.
_________ ________ _____ _________ _______ __________.
_________ ________ ___ ________ _____.
____ _____ _______ ____.
Skip in 10
To show that ( P_1(x) ) is orthogonal to ( [P_n(x)]^2 ) on the interval ((-1, 1)), we need to verify that [ \int_{-1}^{1} P_1(x) [P_n(x)]^2 , dx = 0 ] where ( P_n(x) ) are the Legendre polynomials. Recall that ( P_1(x) = x ) and the Legendre polynomials satisfy the orthogonality relation [ \int_{-1}^{1} P_m(x) P_n(x) , dx = 0 \quad \text{for } m \neq n. ] Consider the integrand ( x
_______ ___ ____ _________ ________.________ ______ ___ _____ ______ ______ ___ _____ _____.
______ _________ __________ ___ _____ _________ ______ ____.
_________ ______ ___ ______ ______ __________.
________ ___ __________ ____ ______.
_____ _________ __________ _______ ___ __________ _____.
_________ ________ __________ _______ ________.
______ _______ ___ _______ ______.
___ __________ __________ ____ _____ __________ __________ ______.
__________ __________ __________ ____ __________ ______.
______ _____ ___ _____ _____ _______ ________ ____ ___ ______.
________ __________ ____ ______ ____ ___ __________.
__________ __________ ____ ______ __________ __________ _____ _____ _______ __________ ____ _________.
___ _______ __________ _________ _____ ___ _________ ____ ____ ____.
______ _______ __________ _________ ___ ____ ______.
_________ ________ _____ _________ _______ __________.
_________ ________ ___ ________ _____.
____ _____ _______ ____.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.
Related Questions
Determine the Fourier transform of the function :
विचित्रता के प्रति फलन
का लौराँ श्रेणी प्रसार प्राप्त कीजिए।
विषम-हर्मिटी आव्यूह, लांबिक आव्यूह और ऐकिक आव्यूह को उदाहरण सहित परिभाषित कीजिए।
सिद्ध कीजिए कि समीकरण के मूल, कोटि 4 का चक्रीय समूह बनाते हैं।
अवशिष्ट विधि का उपयोग कर, सिद्ध करें कि :
Define skew-hermitian matrix, orthogonal matrix and unitary matrix with an example of each.
सिद्ध करें कि :