Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals
Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials {λn(k)(x)} which are defined by the generating function ∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−z)12(x+k), |z|<1.
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000555 |
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| _version_ | 1849470178353479680 |
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| author | P. A. Lee |
| author_facet | P. A. Lee |
| author_sort | P. A. Lee |
| collection | DOAJ |
| description | Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials {λn(k)(x)} which are defined by the generating function ∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−z)12(x+k), |z|<1. |
| format | Article |
| id | doaj-art-dc9685a731564e97ada0eb828c47fa90 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dc9685a731564e97ada0eb828c47fa902025-08-20T03:25:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013476177110.1155/S0161171280000555Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominalsP. A. Lee0Department of Mathematics, University of Malaya, Kuala Lumpur 22-11, MalaysiaUsing the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials {λn(k)(x)} which are defined by the generating function ∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−z)12(x+k), |z|<1.http://dx.doi.org/10.1155/S0161171280000555Meixner-Pollaczek polynomialsorthogonal polynomialsbilinear summation formulabivariate distributioncanonical expansionRunge identityG-functions. |
| spellingShingle | P. A. Lee Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals International Journal of Mathematics and Mathematical Sciences Meixner-Pollaczek polynomials orthogonal polynomials bilinear summation formula bivariate distribution canonical expansion Runge identity G-functions. |
| title | Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals |
| title_full | Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals |
| title_fullStr | Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals |
| title_full_unstemmed | Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals |
| title_short | Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals |
| title_sort | probabilistic derivation of a bilinear summation formula for the meixner pollaczek polynominals |
| topic | Meixner-Pollaczek polynomials orthogonal polynomials bilinear summation formula bivariate distribution canonical expansion Runge identity G-functions. |
| url | http://dx.doi.org/10.1155/S0161171280000555 |
| work_keys_str_mv | AT palee probabilisticderivationofabilinearsummationformulaforthemeixnerpollaczekpolynominals |