J₀(0) = 1 is the maximum value of the Bessel function of the first kind. It occurs when the order ν = 0 and x = 0. To calculate this, follow these steps:
Substitute ν = 0 and x = 0 into the integrand cos(ντ - x sin(τ)) to get cos(0) = 1.
Evaluate the integral ∫1 ∙ dτ to get [τ].
Apply the lower limit 0 and the upper limit π to [τ] to get [π-0] = π.
Divide by π to get π/π = 1.
Verify this result using Omni's Bessel function calculator!
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