This code gives the roots (lambda-values) of eq1
by using iteration.
eq1[n_, β_, λ_] := Hypergeometric1F1[1/4 (2 - λ/β), n + 1, β]
rootslist[n_Integer, k_Integer, β_] :=
Rest @ FoldList[FindRoot[eq1[n, #2, λ] == 0, {λ, #1}][[1, 2]] &
BesselJZero[n, k]^2, Range @ β]
Table[rootslist[n, 1, 30], {n, 0, 4}]
The table contains all the λ-values for each β from 1 to 30. Using this I want to know how to find a table with $\frac{\lambda}{\beta}$ values?
For example, I have produced the following table
{6., 6.63583, 7.64905, 8.97767, 10.5495, 12.2936, 14.1498, 16.0735, 18.0349, 20.0161, 22.0073, 24.0032, 26.0014, 28.0006, 30.0003, 32.0001, 34., 36., 38., 40., 42., 44., 46., 48., 50., 52., 54., 56., 58., 60.},
for $n=0$.
How can I get
$\{\frac{6.}{1}, \frac{6.63583}{2}, \frac{7.64905}{3}, \frac{8.97767}{4}, \frac{10.5495}{5}, \frac{12.2936}{6}, \frac{14.1498}{7}, \frac{16.0735}{8},\frac{ 18.0349}{9}, \frac{20.0161}{10}, \frac{22.0073}{11}, \frac{24.0032}{12}, \frac{26.0014}{13},\frac{ 28.0006}{14}, \frac{30.0003}{15},\frac{ 32.0001}{16}, \frac{34.}{17}, \frac{36.}{18}, \frac{38.}{19}, \frac{40.}{20}, \frac{42.}{21}, ..., \frac{60.}{30}\}\text{?}$