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You can specify multiple channels as well.

Similarly, you can use the channel override syntax with encrypted credentials as well.

This is how a setup with encrypted credentials could look like:

Once everything’s setup, push a new commit and you should see something like the screenshot below:

Turn pull request notifications off by adding on_pull_requests: false to the slack section of your .travis.yml :

Customize the notification message by editing the template, as in this example:

The default template for push builds is:

while the default template for pull request builds is:

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for more information on message formatting.

You can define webhooks to be notified about build results:

Or multiple URLs:

As with other notifications types you can specify when webhook payloads will be sent:

Webhooks are delivered with a application/x-www-form-urlencoded content type using HTTP POST, with the body including a payload parameter that contains the JSON webhook payload in a URL-encoded format.

Here is the payload sent to the Travis CI documentation application :

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You will see one of the following values in the status / result fields that represent the state of the build.

Additionally a message will be present in the status_message / result_message fields that further describe the status of the build.

The type field can be used to find the event type that caused this build to run. Its value is one of push , pull_request , cron , or api . For pull requests, the type field will have the value pull_request , and a pull_request_number field is included too, pointing to the pull request’s issue number on GitHub.

To quickly identify the repository involved, we include a Travis-Repo-Slug header, with a format of account/repository , so for instance travis-ci/travis-ci .

To ensure the integrity of your workflow, we strongly encourage you to verify the POST request before acting on it.

The POST request comes with the custom HTTP header Signature . Using the published SSL public key, you can verify the signature of the payload.

WebhookSignatureVerifier is a small Sinatra app which shows you how this works.

This documentation site receives a webhook notification, verifies the request and updates the Gist showing the payload example above. See the code .

Generating function transformations can come into play when we seek to express a generating function for the sums

in the form of S ( z ) = g ( z ) A ( f ( z ) ) {\displaystyle S(z)=g(z)A(f(z))} involving the original sequence generating function. For example, if the sums s n := k 0 ( n + k m + 2 k ) a k {\displaystyle s_{n}:=\sum _{k\geq 0}{\binom {n+k}{m+2k}}a_{k}} , then the generating function for the modified sum expressions is given by S ( z ) = z m ( 1 z ) m + 1 A ( z ( 1 z ) 2 ) {\displaystyle S(z)={\frac {z^{m}}{(1-z)^{m+1}}}A\left({\frac {z}{(1-z)^{2}}}\right)} [24] (see also the binomial transform and the Stirling transform ).

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