English: For a moment imagine that y(x,0) is some arbitrary function of x, then what you have on right hand side is an infinite series in terms of sin x , sin So, that should remind you of Fourier series and similarly if you look at this ν as a function of x,0 , again just for a moment if you imagine that this is some arbitrary function this entire expression looks like a Fourier series.
Telugu: y(x,0) అనేది x యొక్క ఆర్బిటరీ ఫంక్షన్(arbitrary function) అని ఒక్క క్షణం ఊహించుకోండి, ఆపై మీకు కుడి వైపున ఉన్నది sin x , sin $\frac{\omega x}{c}$ పరంగా ఇన్ఫినిటీ సిరీస్(infinite series).