About the Project
NIST

Parseval-type formulas

AdvancedHelp

(0.001 seconds)

1—10 of 225 matching pages

1: 1.14 Integral Transforms
Parseval’s Formula
(1.14.8) is Parseval’s formula. …
Parseval’s Formula
Parseval-type Formulas
2: 2.5 Mellin Transform Methods
The inversion formula is given by … When x = 1 , this identity is a Parseval-type formula; compare §1.14(iv). … This is allowable in view of the asymptotic formulaNow suppose that there is a real number p j k in D j k such that the Parseval formula (2.5.5) applies and …
3: 27.20 Methods of Computation: Other Number-Theoretic Functions
The recursion formulas (27.14.6) and (27.14.7) can be used to calculate the partition function p ( n ) for n < N . … A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function τ ( n ) , and the values can be checked by the congruence (27.14.20). …
4: Howard S. Cohl
Howard is the project leader for the NIST Digital Repository of Mathematical Formulae seeding and development projects. In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-free full semantic information for mathematical formulae.
5: Preface
Abramowitz and Stegun’s Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables is being completely rewritten with regard to the needs of today. …The authors will review the relevant published literature and produce approximately twice the number of formulas that were contained in the original Handbook. …
6: 5.5 Functional Relations
§5.5(ii) Reflection
5.5.3 Γ ( z ) Γ ( 1 - z ) = π / sin ( π z ) , z 0 , ± 1 , ,
§5.5(iii) Multiplication
Duplication Formula
Gauss’s Multiplication Formula
7: 24.6 Explicit Formulas
§24.6 Explicit Formulas
24.6.6 E 2 n = k = 1 2 n ( - 1 ) k 2 k - 1 ( 2 n + 1 k + 1 ) j = 0 1 2 k - 1 2 ( k j ) ( k - 2 j ) 2 n .
24.6.7 B n ( x ) = k = 0 n 1 k + 1 j = 0 k ( - 1 ) j ( k j ) ( x + j ) n ,
24.6.12 E 2 n = k = 0 2 n 1 2 k j = 0 k ( - 1 ) j ( k j ) ( 1 + 2 j ) 2 n .
8: 27.5 Inversion Formulas
§27.5 Inversion Formulas
which, in turn, is the basis for the Möbius inversion formula relating sums over divisors: … Special cases of Möbius inversion pairs are: … Other types of Möbius inversion formulas include: …
9: 3.5 Quadrature
Gauss–Legendre Formula
Gauss–Chebyshev Formula
Gauss–Laguerre Formula
a complex Gauss quadrature formula is available. …
10: Possible Errors in DLMF
One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula. …