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Why is this the difference between the standard paper equation of local reaction and the implementation of tensor flow?

I met this equation in Alex paper on local normalization of the answer:enter image description here

As we see above, the power rises after calculating the sum, multiply it by alpha and then add after adding k.

However, I see that in the TensorFlow documentation it appears as

sqr_sum[a, b, c, d] =
  sum(input[a, b, c, d - depth_radius : d + depth_radius + 1] ** 2)
output = input / (bias + alpha * sqr_sum ** beta)

where beta rises only for the amount.

Why is there a discrepancy?

Also, when I looked at the TensorFlow code itself, I saw this:

output[b, r, c, d] /= (
            np.power(bias + alpha * np.sum(patch * patch), beta))

which looks right?

I am a bit confused. Can someone correct me please?

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Source: https://habr.com/ru/post/1623917/

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