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Formula:1351

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Digital Library of Mathematical Functions ID 3.8.E12

z n + 1 = z n - f ⁢ ( z n ) f ′ ⁢ ( z n ) - ( f ′′ ⁢ ( z n ) ⁢ f ⁢ ( z n ) / ( 2 ⁢ f ′ ⁢ ( z n ) ) ) . subscript 𝑧 𝑛 1 subscript 𝑧 𝑛 𝑓 subscript 𝑧 𝑛 superscript 𝑓 ′ subscript 𝑧 𝑛 superscript 𝑓 ′′ subscript 𝑧 𝑛 𝑓 subscript 𝑧 𝑛 2 superscript 𝑓 ′ subscript 𝑧 𝑛 {\displaystyle{\displaystyle z_{n+1}=z_{n}-\frac{f(z_{n})}{f^{\prime}(z_{n})-(% f^{\prime\prime}(z_{n})f(z_{n})/(2f^{\prime}(z_{n})))}.}}


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