How do you find the second solution in Frobenius?

We collect terms and write everything as a single series. The obtained series must be zero. Setting the first coefficient (usually the coefficient of xr) in the series to zero we obtain the indicial equation, which is a quadratic polynomial in r. and solve for all bk to obtain the second solution.

How do you solve a Frobenius equation?

The method is called the Frobenius method, named after the mathematician Ferdinand Georg Frobenius. x2y + P xy + Qy = 0, (5) has a singular point at x = 0, and we know that a solution for x > 0 is given by y(x) = xr = er log x, (6) where r is a root of the characteristic (or auxiliary) equation r2 + (P − 1)r + Q = 0.

What is the difference between power series and Frobenius method?

The Frobenius method is a generalisation of the power series method. It extends the power series method to include negative and fractional powers. It also allows an extension involving logarithm terms.

How do you write an indicial equation?

a0(2r(r-1) + r) = 0 => r(2r-1) = 0, an equation which is called the indicial equation. The roots of this equation, r1 = 1/2 and r2 = 0, are called the exponents of the equation. You use each of these to write the recurrence relations in terms of n only.

What is an indicial equation in maths?

indicial equation in American English noun. Math. an equation that is obtained from a given linear differential equation and that indicates whether a solution in power series form exists for the differential equation.

How do you calculate Frobenius numbers?

There is an explicit formula for the Frobenius number when there are only two different coin denominations, x and y: the Frobenius number is then xy − x − y. If the number of coin denominations is three or more, no explicit formula is known.

What is chicken McNugget Theorem?

The Chicken McNugget Theorem states that for any two relatively prime positive integers ‘m, n’, the greatest integer that cannot be written in the form ‘am+bn’ for non-negative integers a, b is ‘mn-m-n’.

What is the largest number of nuggets that you can’t buy?

43
What is the largest number of McNuggets that you can’t buy with packs of 6, 9 and 20? After putting in their blood, sweat, and tears, the mathematicians found that the answer is 43. You cannot buy 43 nuggets with packs of 6, 9 and 20, but you can buy any amount larger than 43.