Description:
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Some languages have 2 cases of month names - genitive and nominative. Eg in Russian - January have 2 cases - 'Январь' and 'января', depended on month place in string.

'1 January' in Russian must be translated as '1 января'
'January, 1' in Russian must be translated as 'Январь, 1'

But PHP date function have only one case for month name - 'F', that translates to nominative case, and there are no way to translate in genitive case.

There are many workarounds for this problem via custom scripts, also this already implemented in some systems, eq in Russian PHP CMS Bitrix: https://dev.1c-bitrix.ru/api_help/main/functions/date/formatdate.php added 'f' symbol that return month in genitive case.

On some other languages, eg C# - this feature is implemented: https://msdn.microsoft.com/en-us/library/system.globalization.datetimeformatinfo.monthgenitivenames.aspx

Because function date() not use locale, my suggestion is to add new symbol to PHP strtotime() and DateTime::format functions, that will return month name in genitive case with no capital letter. For example, this can be '%L' symbol, that return localized month name in genitive case.

Or maybe community can provide some better solutions for this problem in PHP core.

P.S. Description of problem in Russian language: Правильное склонение месяца в датах через PHP функции strtotime() и DateTime::format в именительном и родительном падежах на русском языке.

Test script:
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<?php
setlocale(LC_TIME, 'ru_RU.UTF-8');
echo strftime('%B %L', strtotime('2000-01-01'));
?>

Expected result:
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Январь января

Actual result:
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Январь %L