?正交多項式是一種數(shù)學(xué)概念，指的是一組滿足特定條件的多項式函數(shù)。它們在數(shù)學(xué)和物理學(xué)中都有重要的應(yīng)用，可以用來描述和解決各種問題。

Orthogonal polynomials, also known as orthogonal functions, are a set of polynomial functions that satisfy certain conditions. They have important applications in mathematics and physics, and can be used to describe and solve various problems.

怎么讀（音標(biāo)）

正交多項式 [zhèng jiāo duō xi shì]

用法

正交多項式可以用來表示不同變量之間的關(guān)系，也可以作為基函數(shù)來展開其他函數(shù)。它們具有良好的性質(zhì)，在數(shù)值計算和近似計算中有廣泛的應(yīng)用。

Orthogonal polynomials can be used to represent relationships between different variables, or as basis functions to expand other functions. They possess good properties and have wide applications in numerical and approximation calculations.

例句1-5句且中英對照

1. 正交多項式在物理學(xué)中被廣泛應(yīng)用，如量子力學(xué)中的諧振子問題。

Orthogonal polynomials are widely used in physics, such as in the harmonic oscillator problem in quantum mechanics.

2. 在數(shù)值計算中，正交多項式可以用來構(gòu)造高效的數(shù)值積分方法。

In numerical calculations, orthogonal polynomials can be used to construct efficient numerical integration methods.

3. 正交多項式具有互相正交和歸一化的性質(zhì)，在解決微分方程和最小二乘問題時十分有用。

The orthogonality and normalization properties of orthogonal polynomials are useful in solving differential equations and least squares problems.

4. 勒讓德多項式是一種常見的正交多項式，它們在物理學(xué)中常用來描述球面上的問題。

Legendre polynomials are a common type of orthogonal polynomials, often used in physics to describe problems on spheres.

5. 貝塞爾函數(shù)可以表示為勒讓德多項式的線性組合，因此也可以看作是一種正交多項式。

Bessel functions can be expressed as linear combinations of Legendre polynomials, and can therefore also be considered as orthogonal polynomials.

同義詞及用法

正交多項式也被稱為正交函數(shù)，它們具有相似的性質(zhì)和應(yīng)用。在不同的領(lǐng)域中，可能會使用不同的名稱來指代正交多項式，但它們都指代同一類函數(shù)。

Synonyms for orthogonal polynomials include orthogonal functions, which have similar properties and applications. In different fields, different names may be used to refer to orthogonal polynomials, but they all refer to the same type of functions.

編輯總結(jié)

正交多項式是一組滿足特定條件的多項式函數(shù)，在數(shù)學(xué)和物理學(xué)中都有重要的應(yīng)用。它們具有良好的性質(zhì)，在數(shù)值計算和近似計算中發(fā)揮著重要作用。熟悉并掌握正交多項式的概念和應(yīng)用，可以幫助我們更好地理解和解決各種數(shù)學(xué)和物理問題。