Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:concept
|
| gptkbp:appearsIn |
Taylor_series_expansions
|
| gptkbp:can_be |
recurrence relations
|
| gptkbp:canLeadTo |
x = 1/2
|
| gptkbp:defines |
Bernoulli's_formula
|
| gptkbp:evaluates |
B_n(x) = rac{1}{n!} rac{d^n}{dx^n} rac{x^n}{e^x - 1}
|
| gptkbp:foodPairing |
B_n(0) = B_n(1)
|
| gptkbp:hasAwards |
B_n(1)_=_1_for_n_=_0
|
| gptkbp:hasRelatedPatent |
physics
|
| gptkbp:hasSpecialty |
orthogonality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bernoulli polynomials
|
| gptkbp:isCitedBy |
B_n(x) = rac{1}{n!} rac{d^n}{dx^n} rac{x^n}{e^x - 1}
|
| gptkbp:isCitedIn |
the context of calculus
|
| gptkbp:isConnectedTo |
analytic number theory
complex analysis zeta function regularization Euler-Maclaurin_formula |
| gptkbp:isIntegratedWith |
power sums
|
| gptkbp:isMaintainedBy |
generating functions
|
| gptkbp:isMarketedAs |
B_n(x) = rac{1}{n!} rac{d^n}{dx^n} rac{x^n}{e^x - 1}
|
| gptkbp:isRelatedTo |
gptkb:Riemann_zeta_function
gptkb:Bézier_curves Fourier series hypergeometric functions Cauchy distribution Lerch transcendent Stirling_numbers |
| gptkbp:isUsedFor |
evaluate integrals
approximate functions solve differential equations generate sequences B_n(x) = rac{1}{n!} rac{d^n}{dx^n} rac{x^n}{e^x - 1} |
| gptkbp:isUsedIn |
data analysis
mathematical physics mathematical modeling signal processing probability theory statistical mechanics numerical analysis combinatorial identities theory of functions approximation theory numerical integration theory of distributions theory of special functions computation of sums finite difference calculus theory of approximation quantum_mechanics |
| gptkbp:isValuedFor |
non-negative integers
|
| gptkbp:offersDegree |
n
|
| gptkbp:orbitalInclination |
B_n(x) = B_n(1-x)
|
| gptkbp:relatedTo |
gptkb:Bernoulli_numbers
|
| gptkbp:stadium |
gptkb:Jacques_Bernoulli
|
| gptkbp:usedIn |
number theory
|