To make something regular or consistent; to bring into conformity with a standard or norm. The government plans to regularise the informal housing sector to ensure all residents have access to basic services.
To make something official or legal, often by following a formal procedure. The company had to regularise the employment status of its temporary workers to comply with new labor laws.
To modify a mathematical expression, model, or equation so as to eliminate singularities or divergences, often by introducing a regulating parameter. The physicists regularised the divergent integral using dimensional regularisation.