[Python] Exponential Moving Average (EMA) calculations in Polars dataframe

I have the following list of 20 values:

values = [143.15,143.1,143.06,143.01,143.03,143.09,143.14,143.18,143.2,143.2,143.2,143.31,143.38,143.35,143.34,143.25,143.33,143.3,143.33,143.36]


In order to find the Exponential Moving Average, across a span of 9 values, I can do the following in Python:

def calculate_ema(values, periods, smoothing=2):
ema = [sum(values[eriods]) / periods]

for price in values[periods:]:
ema.append((price * (smoothing / (1 + periods))) + ema[-1] * (1 - (smoothing / (1 + periods))))
return ema

ema_9 = calculate_ema(values, periods=9)


[143.10666666666668,
143.12533333333334,
143.14026666666666,
143.17421333333334,
143.21537066666667,
143.24229653333333,
143.26183722666667,
143.25946978133334,
143.27357582506667,
143.27886066005334,
143.28908852804267,
143.30327082243414]


The resulting list of EMA values is 12 items long, the first value [0] corresponding to the 9th [8] value from values.

Using Pandas and TA-Lib, I can perform the following:

import pandas as pd
import talib as ta

df_pan = pd.DataFrame(
{
'value': values
}
)

df_pan['ema_9'] = ta.EMA(df_pan['value'], timeperiod=9)

df_pan


value ema_9
0 143.15 NaN
1 143.10 NaN
2 143.06 NaN
3 143.01 NaN
4 143.03 NaN
5 143.09 NaN
6 143.14 NaN
7 143.18 NaN
8 143.20 143.106667
9 143.20 143.125333
10 143.20 143.140267
11 143.31 143.174213
12 143.38 143.215371
13 143.35 143.242297
14 143.34 143.261837
15 143.25 143.259470
16 143.33 143.273576
17 143.30 143.278861
18 143.33 143.289089
19 143.36 143.303271


The Pandas / TA-Lib output corresponds with that of my Python function.

However, when I try to replicate this using funtionality purely in Polars:

import polars as pl

df = (
pl.DataFrame(
{
'value': values
}
)
.with_columns(
pl.col('value').ewm_mean(span=9, min_periods=9,).alias('ema_9')
)
)

df


I get different values:

value ema_9
f64 f64
143.15 null
143.1 null
143.06 null
143.01 null
143.03 null
143.09 null
143.14 null
143.18 null
143.2 143.128695
143.2 143.144672
143.2 143.156777
143.31 143.189683
143.38 143.229961
143.35 143.255073
143.34 143.272678
143.25 143.268011
143.33 143.280694
143.3 143.284626
143.33 143.293834
143.36 143.307221


Can anyone please explain what adjustments I need to make to my Polars code in order get the expected results?

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