“Bessel function”的概念、定义、翻译、参考文献-科学参考

Bessel function

Physics

A type of function that occurs as a solution to problems involving waves in systems with cylindrical symmetry. Bessel functions have been extensively studied and tabulated and are used in many branches of mathematical physics. They are named after the German astronomer Friedrich Wilhelm Bessel (1784–1846).

Mathematics

Functions that provide solutions to Bessel’s equation. Bessel’s functions of the first kind are of the form $J_{n} (z) = \sum_{r = 0}^{\infty} \frac{{(- 1)}^{r}}{r! Γ (n + r + 1)} {(\frac{z}{2})}^{n + 2 r}$ where Γ‎ denotes the gamma function. In particular, J₀ $(z) = \sum_{r = 0}^{\infty} \frac{{(- 1)}^{r}}{{(r!)}^{2}} {(\frac{z}{2})}^{2 r} .$

Chemical Engineering

A type of function denoted by the letter J to represent the solution to a type of differential equation that has independent solutions which can be expressed as infinite series. An example is the harmonic equation:
$\frac{d^{2} h}{d r^{2}} + ω^{2} h = 0$

The general solution is $h (ω r) = A C (ω r) + B S (ω r)$ where A and B are constants of integration. The solutions form an infinite series and are listed in tables and plotted. They are used in the study of fluid mechanics and heat transfer, and named after German astronomer Friedrich Wilhelm Bessel (1784–1846).

单词	Bessel function
释义	Bessel function Physics A type of function that occurs as a solution to problems involving waves in systems with cylindrical symmetry. Bessel functions have been extensively studied and tabulated and are used in many branches of mathematical physics. They are named after the German astronomer Friedrich Wilhelm Bessel (1784–1846). Mathematics Functions that provide solutions to Bessel’s equation. Bessel’s functions of the first kind are of the form $J_{n} (z) = \sum_{r = 0}^{\infty} \frac{{(- 1)}^{r}}{r! Γ (n + r + 1)} {(\frac{z}{2})}^{n + 2 r}$ where Γ‎ denotes the gamma function. In particular, J₀ $(z) = \sum_{r = 0}^{\infty} \frac{{(- 1)}^{r}}{{(r!)}^{2}} {(\frac{z}{2})}^{2 r} .$ Chemical Engineering A type of function denoted by the letter J to represent the solution to a type of differential equation that has independent solutions which can be expressed as infinite series. An example is the harmonic equation: $\frac{d^{2} h}{d r^{2}} + ω^{2} h = 0$ The general solution is $h (ω r) = A C (ω r) + B S (ω r)$ where A and B are constants of integration. The solutions form an infinite series and are listed in tables and plotted. They are used in the study of fluid mechanics and heat transfer, and named after German astronomer Friedrich Wilhelm Bessel (1784–1846).
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