Higher Order Bernoulli and Euler Numbers

... can make the individual terms in my sum always correspond to such groups of Dyck words. Hopefully this will lead to a bijective proof of my formula. ...

... can make the individual terms in my sum always correspond to such groups of Dyck words. Hopefully this will lead to a bijective proof of my formula. ...

Kevin McGown: Computing Bernoulli Numbers Quickly

... what we will describe was gleaned from the PARI-2.2.11.alpha source code. The algorithm this version of PARI uses to compute Bernoulli numbers was written by Henri Cohen and later refined by Karim Belabas; it was originally designed to speed up the computation of zeta values. For real s > 1, Euler d ...

... what we will describe was gleaned from the PARI-2.2.11.alpha source code. The algorithm this version of PARI uses to compute Bernoulli numbers was written by Henri Cohen and later refined by Karim Belabas; it was originally designed to speed up the computation of zeta values. For real s > 1, Euler d ...

Lecture 1: Worksheet Triangular numbers 1 3 6 10 15 21 36 45

... We stack now spheres onto each other building n layers and count the number of spheres. The number sequence we get are called tetrahedral numbers. ...

... We stack now spheres onto each other building n layers and count the number of spheres. The number sequence we get are called tetrahedral numbers. ...

Problem Solving Techniques

... 100. At every stage, two are selected, erased from the board, and their sum plus product is added to the list on the board. At any stage, you’re free to choose any two numbers. When the board is reduced to a single number, what possible values can ...

... 100. At every stage, two are selected, erased from the board, and their sum plus product is added to the list on the board. At any stage, you’re free to choose any two numbers. When the board is reduced to a single number, what possible values can ...

Integers and the Number Line

... arrowheads indicate that the line and the set of numbers continue ...

... arrowheads indicate that the line and the set of numbers continue ...

CBSE 8th Class Mathematics Chapter Rational Number CBSE TEST PAPER - 02

... 4. The product of two rational numbers is always a _______. (a) whole numbers ...

... 4. The product of two rational numbers is always a _______. (a) whole numbers ...

Bernoulli Law of Large Numbers and Weierstrass` Approximation

... Bernoulli Law of Large Numbers and Weierstrass’ Approximation Theorem Márton Balázs∗ and Bálint Tóth∗ October 13, 2014 This little write-up is part of important foundations of probability that were left out of the unit Probability 1 due to lack of time and prerequisites. Here we give an elementa ...

... Bernoulli Law of Large Numbers and Weierstrass’ Approximation Theorem Márton Balázs∗ and Bálint Tóth∗ October 13, 2014 This little write-up is part of important foundations of probability that were left out of the unit Probability 1 due to lack of time and prerequisites. Here we give an elementa ...

PDF

... A k-superperfect number n is an integer such that σ k (n) = 2n, where σ k (x) is the iterated sum of divisors function. For example, 16 is 2-superperfect since its divisors add up to 31, and in turn the divisors of 31 add up to 32, which is twice 16. At first Suryanarayana only considered 2-superper ...

... A k-superperfect number n is an integer such that σ k (n) = 2n, where σ k (x) is the iterated sum of divisors function. For example, 16 is 2-superperfect since its divisors add up to 31, and in turn the divisors of 31 add up to 32, which is twice 16. At first Suryanarayana only considered 2-superper ...

CounterExamples (Worksheet)

... a. The sum of two odd numbers is even. b. The sum of two even numbers is even. c. The product of two odd numbers is even. d. The product of two even numbers is even. 2. Jim says ‘Prime numbers are always odd’. Prove that Jim is wrong. 3. ‘The square root of a number is always smaller than the number ...

... a. The sum of two odd numbers is even. b. The sum of two even numbers is even. c. The product of two odd numbers is even. d. The product of two even numbers is even. 2. Jim says ‘Prime numbers are always odd’. Prove that Jim is wrong. 3. ‘The square root of a number is always smaller than the number ...