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Mathematica > Mathematics and Algorithms > Calculus > Discrete Calculus > Recurrence and Sum Functions > NorlundB >
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NorlundB

NorlundB
gives Nørlund polynomials of degree n in a.
NorlundB
gives generalized Bernoulli polynomials .
MORE INFORMATION
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Nørlund polynomials satisfy the generating function relation .
  • The generalized Bernoulli polynomials satisfy the generating function relation .
  • The Bernoulli numbers are given by . Generalized Bernoulli numbers are given by higher integer values of a.
  • NorlundB can be evaluated to arbitrary numerical precision.
  • NorlundB automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (2)
First 5 Nørlund polynomials:
Generalized Bernoulli polynomials:
First 5 Nørlund polynomials:
In[1]:=
Click for copyable input
Out[1]=
 
Generalized Bernoulli polynomials:
In[1]:=
Click for copyable input
Out[1]=
Scope   (3)
NorlundB threads element-wise over lists:
Plot Nørlund polynomials:
TraditionalForm formatting:
Applications   (4)
Higher-order generalized Bernoulli numbers:
First 10 Nørlund numbers:
Compare with their integral definition:
Stirling numbers:
Expand ratio of Gamma functions at infinity:
Compare with direct expansion:
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