Integral representations for the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and the generalized Bessel polynomials
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Bibliographic record
Abstract
Motivated essentially by their potential for applications in the mathematical, physical, and statistical sciences, the object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing the main results presented here, the corresponding integral representations are derived for familiar simpler classes of hypergeometric polynomials such as (for example) the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and generalized Bessel polynomials. Each of the integral representations derived in this paper may be also viewed as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
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Full frame distilled prediction
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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