The

-order Taylor series expansion function of

is of the form

. At

, this is the Maclaurin series,

. The differential transformation

of the function

is given by

. The differential inverse transform of

is defined by

. Table 1 in [2] gives a list of properties of the differential transformation. For instance, if

then

.

[1] M. J. Jang, C. L. Chen, and Y. C. Liu, "Analysis of the Response of a Strongly Nonlinear Damped System Using a Differential Transformation Technique,"

*Applied Mathematics and Computation*,

**88**(2–3) 1997 pp. 137–151. doi:

10.1016/S0096-3003(96)00308-6.

[2] C. L. Chen and Y. C. Liu, "Solution of Two-Boundary-Value Problems Using the Differential Transformation Method,"

*Journal of Optimization Theory and Applications*,

**99**(1), 1998 pp. 23–35. doi:

10.1023/A:1021791909142.

[3] M. J. Jang, C. L. Chen, and Y. C. Liu, "On Solving the Initial-Value Problems Using the Differential Transformation Method,"

*Applied Mathematics and Computation*,

**115**(2–3), 2000 pp. 145–160. doi:

10.1016/S0096-3003(99)00137-X.

[4] A. A. Joneidi, D. D. Ganji, and M. Babaelahi, "Differential Transformation Method to Determine Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity,"

*International Communications in Heat and Mass Transfer*,

**36**(7), 2009 pp. 757–62. doi:

10.1016/j.icheatmasstransfer.2009.03.020.