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Matematikada Tans funktsiyasi sifatida belgilanadi^[1]

${ displaystyle operatorname {Tanc} (z) = { frac { tan (z)} {z}}}$

Tanc 2D fitnasi

Tanc '(z) 2D uchastkasi

Tanc integral 2D uchastkasi

Tanc integral 3D syujeti

Murakkab tekislikdagi xayoliy qism

• ${ Displaystyle operator nomi {Im} chap ({ frac { tan (x + iy)} {x + iy}} o'ng)}$

Murakkab tekislikdagi haqiqiy qism

• ${ displaystyle operator nomi {Re} chap ({ frac { tan chap (x + iy o'ng)} {x + iy}} o'ng)}$

mutlaq kattalik

• ${ displaystyle left | { frac { tan (x + iy)} {x + iy}} right |}$

Birinchi tartibli lotin

• ${ displaystyle { frac {1 - ( tan (z)) ^ {2}} {z}} - { frac { tan (z)} {z ^ {2}}}}$

Hosilaning haqiqiy qismi

• ${ displaystyle - operatorname {Re} chap (- { frac {1 - ( tan (x + iy)) ^ {2}} {x + iy}} + { frac { tan (x + iy) )} {(x + iy) ^ {2}}} o'ng)}$

Hosil qilingan lotin qismi

• ${ Displaystyle - operator nomi {Im} chap (- { frac {1 - ( tan (x + iy)) ^ {2}} {x + iy}} + { frac { tan (x + iy) )} {(x + iy) ^ {2}}} o'ng)}$

hosilaning mutlaq qiymati

• ${ displaystyle left | - { frac {1 - ( tan (x + iy)) ^ {2}} {x + iy}} + { frac { tan (x + iy)} {(x +) iy) ^ {2}}} o'ng |}$

Boshqa maxsus funktsiyalar bo'yicha

• ${ displaystyle operator nomi {Tanc} (z) = { frac {2 , i {{ rm {KummerM}} chap (1, , 2, , 2 , iz o'ng)}} { chap (2 , z + pi o'ng) {{ rm {KummerM}} chap (1, , 2, , i chap (2 , z + pi o'ng) o'ng)}}}}$

• ${ displaystyle operator nomi {Tanc} (z) = { frac {2i operator nomi {HeunB} chap (2,0,0,0, { sqrt {2}} { sqrt {iz}} o'ng) } {(2z + pi) operator nomi {HeunB} chap (2,0,0,0, { sqrt {2}} { sqrt {(i / 2) (2z + pi)}} o'ng)} }}$
• ${ displaystyle operator nomi {Tanc} (z) = { frac {{ rm {WhittakerM}} (0, , 1/2, , 2 , iz)} {{ rm {WhittakerM}} (0 , , 1/2, , i (2z + pi)) z}}}$

Seriyani kengaytirish

${ displaystyle operator nomi {Tanc} z approx chap (1 + { frac {1} {3}} z ^ {2} + { frac {2} {15}} z ^ {4} + { frac {17} {315}} z ^ {6} + { frac {62} {2835}} z ^ {8} + { frac {1382} {155925}} z ^ {10} + { frac { 21844} {6081075}} z ^ {12} + { frac {929569} {638512875}} z ^ {14} + O (z ^ {16}) o'ng)}$

${ displaystyle int _ {0} ^ {z} { frac { tan (x)} {x}} , dx = left (z + { frac {1} {9}} z ^ {3} + { frac {2} {75}} z ^ {5} + { frac {17} {2205}} z ^ {7} + { frac {62} {25515}} z ^ {9} + { frac {1382} {1715175}} z ^ {11} + { frac {21844} {79053975}} z ^ {13} + { frac {929569} {9577693125}} z ^ {15} + O (z ^ {17}) o'ng)}$

Pada taxminiyligi

${ displaystyle operator nomi {Tanc} chap (z o'ng) = chap (1 - { frac {7} {51}} , {z} ^ {2} + { frac {1} {255} } , {z} ^ {4} - { frac {2} {69615}} , {z} ^ {6} + { frac {1} {34459425}} , {z} ^ {8} o'ng) chap (1 - { frac {8} {17}} , {z} ^ {2} + { frac {7} {255}} , {z} ^ {4} - { frac {4} {9945}} , {z} ^ {6} + { frac {1} {765765}} , {z} ^ {8} right) ^ {- 1}}$

Galereya

Tanc abs murakkab 3D

Tanc Im murakkab 3D syujeti

Tanc Re murakkab 3D syujeti

Shuningdek qarang

• Sinhc funktsiyasi
• Tanhc funktsiyasi
• Coshc funktsiyasi

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