What's the 'right' format for the HTTP_PROXY environment variable? Caps or no caps?

There is no central authority who assigns an official meaning to environment variables before applications can use them. POSIX defines the meaning of some variables (PATH, TERM, …) and lists several more in a non-normative way as being in common use, all of them in uppercase. http_proxy and friends isn't one of them.

Unlike basically all conventional environment variables used by many applications, http_proxy, https_proxy, ftp_proxy and no_proxy are commonly lowercase. I don't recall any program that only understands them in uppercase, I can't even find one that tries them in uppercase. Many programs use the lowercase variant only, including lynx, wget, curl, perl LWP, perl WWW::Search, python urllib/urllib2, etc. So for these variables, the right form is the lowercase one.

The lowercase name dates back at least to CERN libwww 2.15 in March 1994 (thanks to Stéphane Chazelas for locating this). I don't know what motivated the choice of lowercase, which would have been unusual even then.

There is no standard and both uppercase and lowercase versions are used depending on the application (also see HTTPS_PROXY, ALL_PROXY, NO_PROXY).

For example:

curl

ENVIRONMENT VARIABLES

  Curl reads and understands the following environment variables:

        http_proxy, HTTPS_PROXY, FTP_PROXY

  They should be set for protocol-specific proxies. General proxy should be
  set with

        ALL_PROXY

  A comma-separated list of host names that shouldn't go through any proxy is
  set in (only an asterisk, '*' matches all hosts)

        NO_PROXY

git

http.proxy
   Override the HTTP proxy, normally configured using the http_proxy, https_proxy, 
   and all_proxy environment variables (see curl(1)). [..]

Python

urllib.request.getproxies() supports both lowercase and uppercase variants.

It also mentions a security issue:

If the environment variable REQUEST_METHOD is set, which usually indicates your script is running in a CGI environment, the environment variable HTTP_PROXY (uppercase _PROXY) will be ignored. This is because that variable can be injected by a client using the “Proxy:” HTTP header. If you need to use an HTTP proxy in a CGI environment, either use ProxyHandler explicitly, or make sure the variable name is in lowercase (or at least the _proxy suffix).

---

Some applications allow NO_PROXY to contain stars/ip-ranges while others do not.

---

So

export https_proxy=$http_proxy HTTP_PROXY=$http_proxy HTTPS_PROXY=$http_proxy NO_PROXY=$no_proxy

should have you covered.