Volume Integral Orthogonal Polynomials

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SUMMARY

The discussion focuses on evaluating a specific integral related to Volume Integral Orthogonal Polynomials, particularly involving complex exponentials that yield a Kronecker Delta. The participant questions whether the Delta can be integrated over phi space, suggesting that it can be replaced by a constant factor without affecting orthogonality. The conversation emphasizes the importance of understanding the implications of the Kronecker Delta in this context.

PREREQUISITES
  • Understanding of Volume Integral Orthogonal Polynomials
  • Familiarity with complex exponentials in mathematical analysis
  • Knowledge of Kronecker Delta properties
  • Basic principles of orthogonality in function spaces
NEXT STEPS
  • Research the properties of Volume Integral Orthogonal Polynomials
  • Study the application of Kronecker Delta in integrals
  • Learn about the implications of orthonormality in polynomial spaces
  • Explore advanced techniques for evaluating integrals involving complex functions
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Mathematicians, physicists, and students studying advanced calculus or functional analysis, particularly those interested in orthogonal polynomials and integral evaluations.

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Hello.

Homework Statement


Basically I want to evaluate the integral as shown in this document:
View attachment integral.pdf


Homework Equations





The Attempt at a Solution


The integral with the complex exponentials yields a Kronecker Delta.
My question is whether this Delta can be taken inside the integral over phi space?
 
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I think so. That is to say you can simply replace p by m and forget about ##\theta##.
Check for a possible constant factor in case you want to look at orthonormality. For orthogonality you don't have to bother.
 
Thanks
 

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