Is it permissible to pray in trousers that have a foul odor resulting from multiple emissions of wind, without being soiled by feces?

The presence of gas in the trousers does not affect the validity of the prayer because gas is pure, even if it invalidates ablution (wudu'). It is not legislated to perform istinja' (washing after defecation or urination) from it. Sheikh al-Islam said: "Gas from the anus is pure, and its acquisition of the smell of impurity does no harm." In Kashshaf al-Qina', it states: "Istinja' or istijmar (using stones or other pure materials for cleansing) is obligatory for everything that exits [from the private parts] except gas, due to his (peace be upon him) saying: 'He who performs istinja' from gas is not one of us.'"