Qualified pharmacist Trupti Patel, 35, appeared before Reading Crown Court accused of murdering her daughter Mia, aged 22 days, and her sons Jamie, aged 15 days, and Amar, aged three months.
The alleged murders took place between December 1997 and June 2001.
Mrs Patel, who at the time of the deaths was living in Maidenhead, Berkshire, denies all the charges.
Opening the case against Mrs Patel, prosecuting counsel Paul Dunkels QC said: "For a mother to kill her own children in this way is against nature and instinct as we would normally understand it.
"But the prosecution say that the evidence will demonstrate that Trupti Patel must have done this to her three babies."
Defendant 'hysterical’
Mr Dunkels told the jury of 11 men and one woman that Amar had been born on 5 September, 1997, by elective Caesarean section.
Just 13 and a half weeks later, Amar was pronounced dead at High Wycombe General Hospital after being found by paramedics lying on his back at the family home.
Mrs Patel had called the ambulance and had attempted resuscitation but was "hysterical", the court heard.
A post-mortem examination concluded the death was a typical case of Sudden Infant Death Syndrome, or cot death as it is more commonly known.
Deaths investigated
Mr Dunkels said Mrs Patel and her husband Jayant, also 35, later said that Amar had had "the sniffles" for three to four days before his death.
Jamie Patel was born on 21 June, 1999, also by elective Caesarean section.
He died just 15 days later on 6 July.
Mrs Patel’s daughter Mia was born on 14 May, 2001, again by elective Caesarean section, but she died 22 days later on 5 June.
Mr Dunkels said that after her death her body was transferred to Great Ormond Street Hospital in London so she could be fully examined.
The court was told pathologists found she had a number of fractures to her ribs which were consistent with being squeezed by an adult.
The two pathologists who carried out a post-mortem examination on Mia found evidence consistent with a prolonged episode of interrupted breathing causing a reduction in the supply of oxygen to the body.
Mr Dunkels said that no natural cause had been identified to explain the deaths of Amar, Jamie and Mia but that there were features in all three cases which indicated that someone had obstructed the breathing of each baby.
"Intention to kill"
He said the presence of Mrs Patel was the "compelling factor" in each of the three deaths.
He added: "This mother for some reason felt compelled to attack her babies.
"We cannot say why she went against all the natural instincts of a mother but we suggest that the evidence will show that each time she must have in some way obstructed the breathing of her babies, whether by squeezing the baby's chest or placing something over the baby's nose and mouth or both, taking each of them to the very edge that divides life and death.
"Her intention must have been to kill or cause really serious bodily harm to her babies."
The case was adjourned until Wednesday when the first prosecution witnesses will be called.
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