In this article, we shall extend the result of [17] to discuss second-order partial differentiation of real ternary functions (refer to [7] and [14] for partial differentiation).
@article{bwmeta1.element.doi-10_2478_v10037-010-0015-9, author = {Takao Inou\'e}, title = {Second-Order Partial Differentiation of Real Ternary Functions}, journal = {Formalized Mathematics}, volume = {18}, year = {2010}, pages = {113-127}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0015-9} }
Takao Inoué. Second-Order Partial Differentiation of Real Ternary Functions. Formalized Mathematics, Tome 18 (2010) pp. 113-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0015-9/
[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
[2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
[3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
[4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
[5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
[6] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
[7] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.[Crossref]
[8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
[9] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
[10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
[11] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
[12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
[13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
[14] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.
[15] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
[16] Bing Xie, Xiquan Liang, and Hongwei Li. Partial differentiation of real binary functions. Formalized Mathematics, 16(4):333-338, 2008, doi:10.2478/v10037-008-0041-z.[Crossref]
[17] Bing Xie, Xiquan Liang, and Xiuzhuan Shen. Second-order partial differentiation of real binary functions. Formalized Mathematics, 17(2):79-87, 2009, doi: 10.2478/v10037-009-0009-7.[Crossref]