Orthogonality of Associated Legendre Functions for Noninteger Order and Index

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows an unusual orthogonality relation for Legendre functions of the first kind . In contrast to the well-known situation of integer degree and integer order (associated Legendre polynomials), in this case both degree and order are allowed to take noninteger real values. For fixed , these functions satisfy an orthogonality relation, according to which is 0 whenever is equal to 2 if and , and is given by the formula in any other case.

Contributed by: Axel Schulze-Halberg and John R. Morris (May 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send