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based on an earlier version of the Wolfram Language.
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gives the hyperbolic cosine integral .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where is Euler's constant.
  • CoshIntegral[z] has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, CoshIntegral automatically evaluates to exact values.
  • CoshIntegral can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Evaluate numerically:
Click for copyable input
Click for copyable input
Click for copyable input
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
CoshIntegral threads element-wise over lists:
Simple exact values are generated automatically:
TraditionalForm formatting:
CoshIntegral can be applied to power series:
Find asymptotic series expansion at infinity:
Plot the imaginary part in the complex plane:
Use FullSimplify to simplify expressions containing the hyperbolic cosine integral:
Use FunctionExpand to express CoshIntegral through other functions:
Find a numerical root:
Obtain CoshIntegral from integrals and sums:
CoshIntegral can take large values for moderate-size arguments:
A larger setting for $MaxExtraPrecision can be needed:
Nested integrals:
Plot the logarithm of the absolute value in the complex plane:
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