science
Gottlieb polynomials is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gottlieb polynomials rather than just read about it. In short: In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by ℓ n ( x , λ ) = e − n λ ∑ k ( 1 − e λ ) k ( n k ) ( x k ) = e − n λ 2 F 1 ( − n , − x ; 1 ; 1 − e λ ) {\displaystyle \displaystyle \ell _{n}(x,\lambda )=e^{-n\lambda }\sum _{k}(1-e^{\lambda })^{k}{\binom {n}{k}}{\binom {x}{k}}=e^{-n\lambda }{}_{2}F_{1}(-n,-x;1;1-e^{\lambda })} References Further reading Rainville, Earl D. (…
In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by
ℓ n ( x , λ ) = e − n λ ∑ k ( 1 − e λ ) k ( n k ) ( x k ) = e − n λ
2 F 1 ( − n , − x ; 1 ; 1 − e λ ) {\displaystyle \displaystyle \ell _{n}(x,\lambda )=e^{-n\lambda }\sum _{k}(1-e^{\lambda })^{k}{\binom {n}{k}}{\binom {x}{k}}=e^{-n\lambda }{}_{2}F_{1}(-n,-x;1;1-e^{\lambda })}
References
Further reading Rainville, Earl D. (1960), Special functions, New York: The Macmillan Co., MR 0107725
Start with the simplest possible case. Write down what Gottlieb polynomials claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.
Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gottlieb polynomials before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.
Typical questions about Gottlieb polynomials ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.
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In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by ℓ n ( x , λ ) = e − n λ ∑ k ( 1 − e λ ) k ( n k ) ( x k ) = e − n λ 2 F 1 ( − n , − x ; 1 ; 1 − e λ ) {\displaystyle \displaystyle \ell _{n}(x,\lambda )=e^{-n\lambda }\sum _{k}(1-e^{\lambda })^{k}{\binom {…
Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.
Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.
It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gottlieb polynomials.