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# Kelvin Functions be (G Dataflow)

Version:

Computes the complex Kelvin function of the first kind.

## x

The input argument.

Default: 0

## n

Order of the Kelvin function.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## ber(x) + bei(x)i

Complex value of the Kelvin function of the first kind.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Complex Kelvin Function of the First Kind

The complex-valued Kelvin function of the first kind of order v is a solution of the following complex-valued differential equation.

${x}^{2}\frac{{d}^{4}w}{d{x}^{4}}+x\frac{dw}{dx}-\left(i{x}^{2}+{v}^{2}\right)w=0$

The real and imaginary parts of the Kelvin function of the first kind of order v are solutions of the following differential equation.

${x}^{4}\frac{{d}^{4}w}{d{x}^{4}}+2{x}^{3}\frac{{d}^{3}w}{d{x}^{3}}-\left(1+2{v}^{2}\right)\left({x}^{2}\frac{{d}^{2}w}{d{x}^{2}}-x\frac{dw}{dx}\right)+\left({v}^{4}-4{v}^{2}+{x}^{4}\right)w=0$

The function is defined according to the following intervals for the input values.

$n\in \Im ,\left(x\in \Re \right)$

For any integer value of order n, the function is defined for all real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported
The text passage describes a technical function, the complex Kelvin function of the first kind, including its mathematical definition and the differential equations it solves. It does not contain any specific mathematical questions or answers to such questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
From 12:00 PM - 4:00 PM CST on Thursday, October 18, ni.com will be undergoing system upgrades that may result in temporary service interruption.

We appreciate your patience as we improve our online experience.

# Kelvin Functions be (G Dataflow)

Version:

Computes the complex Kelvin function of the first kind.

## x

The input argument.

Default: 0

## n

Order of the Kelvin function.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## ber(x) + bei(x)i

Complex value of the Kelvin function of the first kind.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Complex Kelvin Function of the First Kind

The complex-valued Kelvin function of the first kind of order v is a solution of the following complex-valued differential equation.

${x}^{2}\frac{{d}^{4}w}{d{x}^{4}}+x\frac{dw}{dx}-\left(i{x}^{2}+{v}^{2}\right)w=0$

The real and imaginary parts of the Kelvin function of the first kind of order v are solutions of the following differential equation.

${x}^{4}\frac{{d}^{4}w}{d{x}^{4}}+2{x}^{3}\frac{{d}^{3}w}{d{x}^{3}}-\left(1+2{v}^{2}\right)\left({x}^{2}\frac{{d}^{2}w}{d{x}^{2}}-x\frac{dw}{dx}\right)+\left({v}^{4}-4{v}^{2}+{x}^{4}\right)w=0$

The function is defined according to the following intervals for the input values.

$n\in \Im ,\left(x\in \Re \right)$

For any integer value of order n, the function is defined for all real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported
user
The text passage describes a technical function, the complex Kelvin function of the first kind, including its mathematical definition and the differential equations it solves. It does not contain any specific mathematical questions or answers to such questions.

TYPE: NO_QUESTION