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SinhIntegral

SinhIntegral[z]
gives the hyperbolic sine integral function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • SinhIntegral[z] is an entire function of z with no branch cut discontinuities.
  • For certain special arguments, SinhIntegral automatically evaluates to exact values.
  • SinhIntegral can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Evaluate numerically:
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Evaluate to high precision:
The precision of the output tracks the precision of the input:
SinhIntegral threads element-wise over lists:
SinhIntegral can take complex number inputs:
Simple exact values are generated automatically:
Arguments simplify automatically:
Find series expansions at infinity:
Give the result for an arbitrary symbolic direction :
SinhIntegral can be applied to power series:
TraditionalForm formatting:
Plot the real part in the complex plane:
Plot the imaginary part in the complex plane:
Use FullSimplify to simplify expressions containing hyperbolic sine integrals:
Find a numerical root:
Obtain SinhIntegral from integrals and sums:
Integrals:
Laplace transform:
SinhIntegral can take large values for moderate-size arguments:
A larger setting for $MaxExtraPrecision can be needed:
In traditional form, parentheses are required:
Nested integrals:
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