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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

List[ED[0{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]]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?

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

List[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?

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?

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Finding multiple roots for the special function Hypergeometric1F1roots of Hypergeometric1F1[]

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Find multi Finding multiple roots for the special function Hypergeometric1F1

I am trying to find the roots, $\lambda$λ, for this equation: Hypergeometric1F1[1/4 (2 - $\lambda$ /$\beta$), n + 1, $\beta$]

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

for certain $\beta$β and nn. Here is my mathematicaMathematica code.

eq[n_, [Beta], [Lambda]] = Hypergeometric1F1[1/4 (2 - [Lambda]/[Beta]), n + 1, [Beta]]

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

Find Rootthe root near $\lambda$ = $\beta$λ = β.

ED[n_, [Beta]_] := [Lambda] /. FindRoot[eq[n, [Beta], [Lambda]] == 0, {[Lambda], [Beta]}]

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

List all $\lambda$λ-values for each value of nn when $\beta$ = 0.00001β = 0.00001

List[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]]

List[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}{5.78319, 14.682, 26.3746, 40.7064, 57.5829, 76.9388, 98.7262, 122.907, 149.453, 178.337, 209.54}

However I supposeI'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}{5.78306, 14.6819, 26.3744, 30.4715, 40.707, 49.2186, 57.5823, 70.8493, 74.8865, 76.9392, 95.2771}

I guess mathematicaMathematica gives only one root, so. How can I don't know how to find also find the 2nd, 3rd, 4th roots, for each value of nn? Please help me! Thank you.

Find multi roots for the special function Hypergeometric1F1

I am trying to find roots, $\lambda$, for this equation: Hypergeometric1F1[1/4 (2 - $\lambda$ /$\beta$), n + 1, $\beta$] for certain $\beta$ and n. Here is my mathematica code.

eq[n_, [Beta], [Lambda]] = Hypergeometric1F1[1/4 (2 - [Lambda]/[Beta]), n + 1, [Beta]]

Find Root near $\lambda$ = $\beta$.

ED[n_, [Beta]_] := [Lambda] /. FindRoot[eq[n, [Beta], [Lambda]] == 0, {[Lambda], [Beta]}]

List all $\lambda$-values for each value of n when $\beta$ = 0.00001

List[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 suppose 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, so I don't know how to find also the 2nd, 3rd, 4th roots, for each value of n? Please help me! Thank you.

Finding multiple roots for the special function 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

List[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?