The first one-day international will be held in Vadodara, western India, on 25 October.
"It was great to see him get his first one-day international hundred, " said Ponting.
The teams will return to the M Chinnaswamy Stadium for the second one-day international on Sunday.
Ryder last played for New Zealand in a one-day international against South Africa in February, 2012.
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Botha took 1-48 during his team's 61-run victory in the fourth one-day international at Port Elizabeth.
The Nottinghamshire seamer suffered a hamstring strain in the final one-day international on Saturday.
Pakistan are scheduled to play England in five one-day international matches, starting at Durham on Friday.
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The former England one-day international hit 13 fours in scoring 105 before falling to Nicky Boje.
The victory also marked a successful return to one-day international cricket for Steve Harmison.
The 24-year-old Australia one-day international averaged more than 50 in his previous Glamorgan spell in 2006.
You can't have Ravi playing in a one-day international and batting at eight, it doesn't make sense.
Jadeja made 5, 359 runs with six centuries in 196 one-day international appearances, and gained 15 Test caps.
While at Hampshire, he made his first appearance for England in 2005 in a one-day international against Bangladesh.
But he has played just a single one-day international and is not even in their World Cup squad.
To play the mighty England in an official one-day international would have been unimaginable just five years ago.
Hayden, 37, scored 8, 625 Test runs at an average of 50.73 and 6, 133 one-day international runs at 43.80.
Davies, 24, was only playing his second one-day international after making his debut in last year's Champions Trophy.
Ireland skipper Trent Johnston was delighted with his team's performance in their historic first one-day international against England.
BBC: SPORT | Cricket | England | Strauss pleased to begin with win
And, at 74-5, the Kiwis were in serious trouble as Sara McGlashan became Colvin's 50th one-day international victim.
The 32-year-old will play his 200th one-day international innings in Wednesday's Asia Cup final in Dhaka against Sri Lanka.
The 33-year-old suffered the injury during the third one-day international against West Indies and missed the final two games.
The second one-day international of this five-match series is at Headingley on Sunday.
Middlesex captain Strauss could debut in Tuesday's first one-day international after opener Vikram Solanki was again dismissed without scoring.
BBC: SPORT | Cricket | Sri v Eng | Strauss stars for England
In only his fifth one-day international, he emerged as the new star of India's cricketing scenario with a tremendous century.
BBC: SPORT | Cricket | International Teams | India | Dashing Dhoni's chance discovery
Edwards played for the West Indies in their one-day international defeat by Australia on Tuesday, but bowled just three overs.
He had a made a rapid recovery after disclocating his shoulder in a one-day international against England on 15 December.
He will set a new record on Wednesday when he leads them for the 194th time in a one-day international.
BBC: SPORT | Cricket | International Teams | New Zealand | Fleming reveals World Cup dream
Since then the game has been revolutionised, with one-day international cricket proving the most popular form of the game worldwide.
The Australians suffered their sixth successive defeat on Wednesday when they lost by one-wicket in a one-day international against Sri Lanka.
England and Pakistan play the fourth, and penultimate, one-day international at Lord's on Monday, with England 2-1 ahead in the series.
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