binomial series expansion

USAGE SUMMARY

The phrase "binomial series expansion" is correct and usable in written English.
It can be used in mathematical or statistical contexts when discussing the expansion of expressions that involve binomials. Example: "The binomial series expansion allows us to express (1 + x)^n as an infinite sum of terms."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion.

Signal Processing

where binomial series expansion has been applied.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

In this paper, parameters of both potential functions are related in terms of factorials and binomial coefficients through implementation of Taylor series expansion and followed by appropriate comparison of corresponding terms.

Chemical Physics

In this paper, we apply the Laplace of the fractional derivative and the expansion coefficients of binomial series to derive the explicit solutions to homogeneous fractional differential equations.

Advances in Difference Equations

The methodology presented here is based chiefly upon some general theorems on (explicit) particular solutions of some families of fractional differential equations with the Laplace transform and the expansion coefficients of binomial series.

Advances in Difference Equations

The fixed and random parameter estimates (along with their SEs) for the multilevel binomial logit link model were calibrated using predictive/penalised quasi-likelihood procedures with second-order Taylor series expansion, as implemented within the MLwiN 2.22.

BMJ Open

A series expansion is completely avoided.

International Journal of Plasticity

The binomial series approximation in the approach, which is crucial for its computational efficiency, is examined and an error analysis is performed.

Journal of Geodynamics

Figure 5 Taylor series expansion piecewise approximation.

EURASIP Journal on Embedded Systems

and Madhava's series expansion (4).

Advances in Difference Equations

If has the series expansion (2.3).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using the "binomial series expansion", ensure that the context clearly indicates the variable or expression being expanded. Specify the conditions for convergence if necessary.

Common error

Avoid using "binomial series expansion" when a different type of series expansion, such as Taylor or Fourier series, is more appropriate for the given mathematical context. Make sure to choose the correct expansion based on the function's properties.

Linguistic Context

The phrase "binomial series expansion" functions as a noun phrase that identifies a specific mathematical technique. It is used to describe the process of expanding a binomial expression into an infinite series, as seen in examples provided by Ludwig.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

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Ludwig's WRAP-UP

The term "binomial series expansion" precisely identifies the mathematical technique of expanding binomial expressions into infinite series. As Ludwig highlights, it's grammatically sound and mainly used in scientific contexts. While alternatives like "binomial expansion" exist, they might lack the specificity needed in technical discussions. Keep in mind the appropriateness of other series expansions in different contexts to avoid confusion. Therefore, understanding its application nuances is crucial for accurate communication in mathematical and scientific domains.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

binomial expansion

Shorter version of the original phrase, omitting "series", maintains the core meaning.

expansion of binomial series

Reverses the order of "binomial" and "series", changing the emphasis slightly.

binomial series development

Uses "development" instead of "expansion", focusing on the process.

series expansion of binomials

Generalizes to multiple binomials rather than a specific series.

power series expansion of a binomial

Specifies the type of series expansion as a power series.

binomial series representation

Emphasizes the result of the expansion as a representation.

generalized binomial expansion

Highlights the generalized form of the binomial expansion.

series approximation of a binomial

Focuses on approximating a binomial using a series.

Taylor series expansion of a binomial

Specifies Taylor series as method of expansion of binomial

Maclaurin series expansion of a binomial

Specifies Maclaurin series as method of expansion of binomial

FAQs

What is the purpose of a "binomial series expansion"?

A "binomial series expansion" is used to express a binomial expression raised to a power as an infinite series. This is particularly useful when the power is not a positive integer.

When is it appropriate to use a "binomial series expansion"?

It's appropriate to use a "binomial series expansion" when you need to approximate or manipulate expressions of the form (1 + x)^n, especially when n is not a positive integer or when |x| < 1 to ensure convergence.

What is the difference between "binomial series expansion" and "binomial theorem"?

The "binomial theorem" applies to positive integer exponents, providing a finite sum. The "binomial series expansion" extends this to non-integer exponents, resulting in an infinite series.

Can I use "binomial expansion" interchangeably with "binomial series expansion"?

Yes, "binomial expansion" is often used as a shorter, more general term, but "binomial series expansion" specifies that the result is a series, especially when dealing with non-integer exponents.