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Matematikada tanhc funktsiyasi sifatida belgilanadi^[1]

${ displaystyle operatorname {tanhc} (z) = { frac { tanh (z)} {z}}}$

Tanhc 2D uchastkasi

Tanhc '(z) 2D uchastkasi

Tanhc integral 2D uchastkasi

Tanhc integral 3D syujeti

Murakkab tekislikdagi xayoliy qism

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

Murakkab tekislikdagi haqiqiy qism

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

mutlaq kattalik

• ${ displaystyle left | { frac { tanh (x + iy)} {x + iy}} o'ng |}$

Birinchi tartibli lotin

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

Hosilaning haqiqiy qismi

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

Hosil qilingan lotin qismi

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

hosilaning mutlaq qiymati

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

Boshqa maxsus funktsiyalar bo'yicha

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

Seriyani kengaytirish

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

${ displaystyle int _ {0} ^ {z} ! { frac { tanh left (x right)} {x}} {dx} = (z - { frac {1} {9}} {z} ^ {3} + { frac {2} {75}} {z} ^ {5} - { frac {17} {2205}} {z} ^ {7} + { frac {62} {25515}} {z} ^ {9} - { frac {1382} {1715175}} {z} ^ {11} + O chap ({z} ^ {13} o'ng))}$

Pada taxminiyligi

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

Galereya

Tanhc abs murakkab 3D

Tanhc Im murakkab 3D syujeti

Tanhc Re murakkab 3D syujeti

Tanhc '(z) Im murakkab 3D syujeti

Tanhc '(z) Re murakkab 3D syujeti

Tanhc '(z) abs murakkab 3D chizmasi

Tanhc abs fitnasi

Tanhc Im fitnasi

Tanhc Re fitnasi

Tanhc '(z) Im fitnasi

Tanhc '(z) abs fitnasi

Tanhc '(z) Re fitna

Tanhc integral abs uchastkasi

Tanhc integral Im 3D syujeti

Tanhc integral Re 3D syujeti

Tanhc integral abs zichligi chizmasi

Tanhc integral Im zichligi chizmasi

Tanhc integral Re zichlik chizmasi

Shuningdek qarang

• Sinhc funktsiyasi
• Tans funktsiyasi
• Coshc funktsiyasi

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