# jacobi.p.recurrences: Recurrence relations for Jacobi polynomials

### Description

This function returns a data frame with n + 1 rows and four named columns containing the coefficient vectors c, d, e and f of the recurrence relations for the order k Jacobi polynomial, P_k^{≤ft( {α ,β } \right)} ≤ft( x \right), and for orders k = 0,\;1,\; … ,\;n.

### Usage

 1 jacobi.p.recurrences(n, alpha, beta, normalized=FALSE) 

### Arguments

 n integer value for the highest polynomial order alpha numeric value for the first polynomial parameter beta numeric value for the second polynomial parameter normalized boolean value which, if TRUE, returns recurrence relations for normalized polynomials

### Value

A data frame with the recurrence relation parameters.

### Author(s)

Frederick Novomestky fnovomes@poly.edu

### References

Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York.

Courant, R., and D. Hilbert, 1989. Methods of Mathematical Physics, John Wiley, New York, NY.

Szego, G., 1939. Orthogonal Polynomials, 23, American Mathematical Society Colloquium Publications, Providence, RI.

jacobi.p.inner.products, pochhammer

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ### ### generate the recurrences data frame for ### the normalized Jacobi P polynomials ### of orders 0 to 10. ### parameter a is 2 and parameter b is 2 ### normalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=TRUE ) print( normalized.r ) ### ### generate the recurrences data frame for ### the unnormalized Jacobi P polynomials ### of orders 0 to 10. ### parameter a is 2 and parameter b is 2 ### unnormalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=FALSE ) print( unnormalized.r ) 

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