Geodesic
General addition formula for meromorphic functions derived from residue theorem
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010) no. 2, pp. 183-191 
Harry Yosh. General addition formula for meromorphic functions derived from residue theorem. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010) no. 2, pp. 183-191. http://geodesic.mathdoc.fr/item/JMAG_2010_6_2_a1/
@article{JMAG_2010_6_2_a1,
     author = {Harry Yosh},
     title = {General addition formula for meromorphic functions derived from residue theorem},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {183--191},
     year = {2010},
     volume = {6},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2010_6_2_a1/}
}
TY  - JOUR
AU  - Harry Yosh
TI  - General addition formula for meromorphic functions derived from residue theorem
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2010
SP  - 183
EP  - 191
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JMAG_2010_6_2_a1/
LA  - en
ID  - JMAG_2010_6_2_a1
ER  - 
%0 Journal Article
%A Harry Yosh
%T General addition formula for meromorphic functions derived from residue theorem
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2010
%P 183-191
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2010_6_2_a1/
%G en
%F JMAG_2010_6_2_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

A meromorphic function is characterized by its singularity, and residues of the poles give us various information regarding the function. In the paper the algebraic relations of residues on some meromorphic functions are considered and a generic form of addition formula is induced from them. As the applications of that formula, the addition formula for rational function, hypergeometric function, elliptic function, and Riemann's Zeta function are studied. Also the general multiplication formula is discussed based on the previous discourse.

[1] E. Picard, Leçons sur quelques équations fonctionnelles, Gauthier-Villars, Paris, 1928

[2] G. N. Watson, Theory of Bessel functions., 2nd ed., Cambridge Univ. Press, Cambridge, 1944 | MR | Zbl

[3] A. Segun, M. Abramowitz, Handbook of Mathematical Functions, Appl. Math. Ser., 55, Nat. Bur. Standards, 1970

[4] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., Oxford University Press, Oxford, 1986 | MR | Zbl

[5] É. P. Stankus, “A Note Concerning the Coefficients of the Laurent Series of the Riemann Zeta Function”, J. Math. Sci., 29:3 (1985), 1302–1305, Springer, New York | DOI | Zbl

[6] N. I. Akhiezer, Elements of the theory of elliptic functions, Amer. Math. Soc., Providence, R.I., 1990 | MR | Zbl

[7] R. S. Lehman, “On Liouville's Function”, Math. Comput., 14 (1960), 311–320 | MR | Zbl