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Applied Mathematical Methods by Bhaskar Dasgupta

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39

Series Solutions and Special Functions

This chapter is devoted to the methods of solution of ordinary differential equations in terms of infinite series. Through these methods, we can arrive at solutions of many vital equations of mathematical physics. Towards the end of the chapter, we also have a brief snapshot of some of these important differential equations. Besides exposing how valuable new functions get defined as solutions of such differential equations, this also clears our way for a smooth discussion on the stimulating theory of Sturm-Liouville problems in the next chapter.

Power Series Method

As we have seen in Chaps. 33 through 35, the systematic analytical methods, i.e. methods that strive to solve an ordinary differential equation ...

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