I Is there a consensus about the meaning of the Christoffel symbols' indices?

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Is there a consensus about the meaning of the Christoffel symbols' indices?
This is from Giancarlo Bernacchi's book "Tensors made easy":

1729945525038.jpeg


And this is from Daniel Fleisch's book "A Student's Guide to Vectors and Tensors":
1729945620727.jpeg

The meaning of the two lower indices is exchanged in the two explanations. Is one of them correct and the other one wrong, or is there no consensus about this?
 
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The Christoffel symbols are given by$$\Gamma^i_{jk}=\frac 12g^{il}\left(
\partial_jg_{kl}
+\partial_jg_{lk}
-\partial_lg_{jk}
\right)$$This is symmetric in the lower indices, so it makes no difference which of those indices you define as doing what.
 
I see, thank you.
 

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