Apply function on cumulative values of pandas series

You can use pd.expanding_apply. Below is a simple example which only really does a cumulative sum, but you could write whatever function you wanted for it.

import pandas as pd

df = pd.DataFrame({'data':[10*i for i in range(0,10)]})

def sum_(x):
    return sum(x)


df['example'] = pd.expanding_apply(df['data'], sum_)

print(df)

#   data  example
#0     0        0
#1    10       10
#2    20       30
#3    30       60
#4    40      100
#5    50      150
#6    60      210
#7    70      280
#8    80      360
#9    90      450