Word Count : 385

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टेलर श्रेणी किसी फलन \( f(x,y) \) का विस्तारित रूप होता है, जो किसी बिंदु \((a,b)\) के आसपास फलन को बहुपद रूप में अभिव्यक्त करता है। टेलर बहुपद का सामान्य रूप द्विवेरीय (bivariate) फलन के लिए होता है: \[ T_3(x,y) = f(a,b) + \frac{\partial f}{\partial x} (a,b) (x-a) + \frac{\partial f}{\partial y} (a,b) (y-b) + \frac{1}{2!} \left[ \frac{\partial^2 f}{\partial x^2} (a,b) (x-a)^2 + 2 \frac{\partial^2 f}{\partial x \partial y} (a,b) (x-a)(y-b) + \frac{\partial^2 f}{\partial y^2} (a,b) (y-b)^2 ________ ___ _____ ____ _______ ____ ___ __________ ______ ______.
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