THE POWER SERIES EXPANSION OF MATHIEU FUNCTION AND ITS INTEGRAL FORMALISM
Abstract
By applying three term recurrence formula (Choun, 2012 \cite{chou2012b}), power series expansions in closed forms of Mathieu equation for an infinite series and their integral forms are constructed.
One interesting observation resulting from the calculations is the fact that a modified Bessel function recurs in each of sub-integral forms: the first sub-integral form contains zero term of $A_n's$, the second one contains one term of $A_n$'s, the third one contains two terms of $A_n$'s, etc. Section 5 contains two additional examples of Mathieu equation.
This paper is 5th out of 10 in series ``Special functions and three term recurrence formula (3TRF).'' See section 6 for all the papers in the series.
One interesting observation resulting from the calculations is the fact that a modified Bessel function recurs in each of sub-integral forms: the first sub-integral form contains zero term of $A_n's$, the second one contains one term of $A_n$'s, the third one contains two terms of $A_n$'s, etc. Section 5 contains two additional examples of Mathieu equation.
This paper is 5th out of 10 in series ``Special functions and three term recurrence formula (3TRF).'' See section 6 for all the papers in the series.
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