You cannot check your purchase history in the game itself, but you can see your purchase history in the Google Play store or the Apple iTunes store.
To see your Android device Google Play Store Purchase history:
https://play.google.com/store/account
To see your iPhone Apple iTunes Store Purchase history:
United States: https://support.apple.com/en-us/HT204088
United Kingdom: https://support.apple.com/en-gb/HT204088
Australia: https://support.apple.com/en-au/HT204088
Canada: https://support.apple.com/en-ca/HT204088
Canada French: https://support.apple.com/fr-ca/HT204088
France: https://support.apple.com/fr-fr/HT204088
Germany: https://support.apple.com/de-de/HT204088
Italy: https://support.apple.com/it-it/HT204088
Spain: https://support.apple.com/es-es/HT204088
Mexico: https://support.apple.com/es-mx/HT204088