Error Functions, Dawson’s and Fresnel Integrals - 7.13 Zeros

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7.13#Ex13 λ = 2 n 𝜆 2 𝑛 {\displaystyle{\displaystyle\lambda=2\sqrt{n}}}
\lambda = 2\sqrt{n}

(sqrt(4*n - 1)) = 2*sqrt(n)
(Sqrt[4*n - 1]) == 2*Sqrt[n]
Skipped - no semantic math Skipped - no semantic math - -
7.13#Ex14 α = ( 2 / π ) ln ( π λ ) 𝛼 2 𝜋 𝜋 𝜆 {\displaystyle{\displaystyle\alpha=(2/\pi)\ln\left(\pi\lambda\right)}}
\alpha = (2/\pi)\ln@{\pi\lambda}

alpha = (2/Pi)*ln(Pi*(sqrt(4*n - 1)))
\[Alpha] == (2/Pi)*Log[Pi*(Sqrt[4*n - 1])]
Failure Failure
Failed [9 / 9]
Result: .421543168
Test Values: {alpha = 1.5, n = 1}

Result: .151839883
Test Values: {alpha = 1.5, n = 2}

... skip entries to safe data
Failed [9 / 9]
Result: 0.4215431680821278
Test Values: {Rule[n, 1], Rule[α, 1.5]}

Result: 0.15183988257850767
Test Values: {Rule[n, 2], Rule[α, 1.5]}

... skip entries to safe data