## What is regular singular point with example?

# What is regular singular point with example?

## What is regular singular point with example?

Example: x2y + 2(ex − 1)y + e−x cos xy = 0, P = x2, Q = 2(ex − 1), R = e−x cos x. x = 0 is a singular point. Since the quotient functions p = xQ/P and q = x2R/P have Taylor Expansions about x = 0, x = 0 is a regular singular point.

## What makes a regular singular point?

Point a is a regular singular point if p1(x) has a pole up to order 1 at x = a and p0 has a pole of order up to 2 at x = a. Otherwise point a is an irregular singular point.

**How do you find a regular singular point?**

Suppose that p(x) and q(x) are polynomials with no common factors. If after reducing p(x) and q(x) to lowest terms, the highest power of x − x0 in the denominator of p(x) is 1 and the highest power of x − x0 in the denominator of q(x) is 2, then x = x0 is a regular singular point of the equation.

### What is regular and irregular singular point?

Regular singular points are well-behaved and defined in terms of the ratio Q(x)/P(x) and R(x)/P(x), where P(x), Q(x), and R(x) are the polynomial coefficients in the differential equation you’re trying to solve. Irregular singular points are a totally different ball game — and one that I don’t get into in this chapter.

### What is regular point in complex analysis?

a mathematical term used in different senses. A regular point of a function f(z) of the complex variable z is a point z0 = x0 + iy0 such that in some neighborhood ǀz – z0ǀ < ρ of it the function is single-valued and can be represented in the form of the series.

**What is singular point in calculus?**

singularity, also called singular point, of a function of the complex variable z is a point at which it is not analytic (that is, the function cannot be expressed as an infinite series in powers of z) although, at points arbitrarily close to the singularity, the function may be analytic, in which case it is called an …

#### What are singular points physics?

#### What are singular points in differential equation?

A differential equation. d2ydx2+p(x)dydx+q(x)y(x)=0. is said to a singular point at x = x0 if at least one of the coefficients, p(x) or q(x) is not holomorphic at this point.

**How do you find irregular singular points?**

Regular and Irregular Singular Points of ODEs Since p2(x) is singular but xp0(x) = -1 is analytic at x0 = 0 (and for all x), x0 is a regular singular point. The point t0 = 0 is an irregular singular point since t2p0(t) is singular at t = 0. Thus x0 = ∞ is an irregular singular point of Airy’s equation.

## What are irregular points?

Regular and Irregular Singular Points of ODEs Other singular points are called irregular. Even at a singular point of an ODE, some (or even all) of its solutions may be analytic, but this is not guaranteed. Classification examples.

## What is meant by regular point?

[¦reg·yə·lər ′pȯint] (mathematics) Any point or a surface that is not a singular point. ordinary point.

**What is meant by singular point?**

a point at which a given function of a complex variable has no derivative but of which every neighborhood contains points at which the function has derivatives.