equation solving - Finding the roots of Hypergeometric1F1[]

I am trying to find the roots, λ, for this equation:

Hypergeometric1F1[1/4 (2 -  λ /β), n + 1, β]

for certain β and n. Here is my Mathematica code.

eq[n_, β_, λ_] = Hypergeometric1F1[1/4 (2 - λ/β), n + 1, β]

Find the root near λ = β.

ED[n_, β_] := λ /. 
  FindRoot[eq[n, β, λ] == 0, {λ, β}]

List all λ-values for each value of n when β = 0.00001

{ED[0, 0.00001], ED[1, 0.00001], ED[2, 0.00001], ED[3, 0.00001], ED[4, 0.00001],
 ED[5, 0.00001], ED[6, 0.00001], ED[7, 0.00001], ED[8, 0.00001], ED[9, 0.00001],
 ED[10, 0.00001]}

Then, I got {5.78319, 14.682, 26.3746, 40.7064, 57.5829, 76.9388, 98.7262, 122.907, 149.453, 178.337, 209.54}

However I'm supposed to get {5.78306, 14.6819, 26.3744, 30.4715, 40.707, 49.2186, 57.5823, 70.8493, 74.8865, 76.9392, 95.2771}

I guess Mathematica gives only one root. How can I also find the 2nd, 3rd, 4th roots, for each value of n?

Comments

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