中文摘要：

目的探讨欧拉（Leonard Euler,1707—1783）对函数概念的贡献。方法文献考证与历史分析。结果欧拉定义的作为解析式的函数概念,使函数概念由几何形态转向代数形态;对超越函数幂级数展式的研究把微积分的研究对象由代数函数扩展为解析函数;对连续性的研究引出了对解析函数的探讨;由物理推理及几何直观催生的非连续函数为微积分的发展提出了新的问题,它的出现预示着微积分研究对象面临着新一轮的扩展;1775年提出的一个更为广泛的函数概念对19世纪的函数概念产生了深刻的影响。结论欧拉对函数概念的发展不仅推动了微积分的发展,而且为现代函数概念的产生做了准备。

英文摘要：

Aim To explore Euler′s contributions to the concept of function.Methods Literature survey and historical analysis.Results The concept of function was transformed from geometrical form to algebraic form caused by Euler′regarding a function as a analytical expression.The research of Euler on power series of transcendental functions extended the object of calculus studying from algebraic function to analytic function.Studying on continuity led to the research about analytic function.The emergence of the non-analytical function,guided by physical considerations and profound geometrical intuition,indicates that the object of calculus studying were subjected to a new extension.A more general concept of function was put forward by Euler in 1775,which effected deeply on the concept of function in 19 century.Conclusion The development of the concept of function contributed by Euler not only Promoted the development of calculus,but also prepared for the emergence of modern concept of function.