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Joshua King came to Cambridge from Hawkshead Grammar School. It was soon evident that the school had produced someone of importance. He became Senior Wrangler, and his reputation in Cambridge was immense. It was believed that nothing less than a Second Newton had appeared. They expected his work as a mathematician to make an epoch in the science. At an early age he became President of Queens’; later, he was Lucasian Professor. He published nothing; in fact, he did no mathematical work. But as long as he kept his health, he was an active and prominent figure in Cambridge, and he maintained his enormous reputation. When he died, it was felt that the memory of such an extraordinary man should not be permitted to die out, and that his papers should be published. So his papers were examined, and nothing whatever worth publishing was found.


7m
answered $\int \sqrt{1+\sin ^2 x} dx$ an elliptic integral?
7h
comment Find the sum of this series
This is a polylogarithm.
7h
comment Using Direct Proof. $1+2+3+\ldots+n = \frac{n(n + 1)}{2}$
See Faulhaber's formulas.
8h
comment How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$
@VladimirReshetnikov: Ascribing a finite value to an otherwise divergent quantity.
17h
comment Computing $\sum_{i=0}^{\infty}\frac{i}{2^{i+1}}$
This is a polylogarithm.
20h
comment Prove that the series is convergent: 1- (1+1/3)/2 + (1+1/3+1/5)/3-…
$\dfrac11+\dfrac13+\dfrac15+\ldots+\dfrac1{2n-1}~ = ~\bigg(\dfrac11+\dfrac12+\dfrac13+\dfrac14+\ldots+\dfrac1{2n}\bigg) - \bigg(\dfrac12+\dfrac14+\ldots+\dfrac1{2n}\bigg)$ $=H_{2n}-\dfrac{H_n}2$, where $H_k$ is the k-th harmonic number. Now all that's left to do is to show that $\displaystyle\sum_{n=1}^\infty(-1)^{n+1}\dfrac{H_{2n}}n = \dfrac{5\pi^2}{48}-\dfrac{\ln^22}4$, and $\displaystyle\sum_{n=1}^\infty(-1)^{n+1}\dfrac{H_n}n = \dfrac{\pi^2}{12}-\dfrac{\ln^22}2$. :-)
20h
comment Prove that the series is convergent: 1- (1+1/3)/2 + (1+1/3+1/5)/3-…
It converges to $\bigg(\dfrac\pi4\bigg)^2$
1d
revised loss of significance errors in mathematical expressions
deleted 16 characters in body
1d
comment Lambert function. Calculate $W(b)$ from $W(a)$.
$W(b)=W(a)+\displaystyle\int_a^bW'(x)~dx$.
1d
reviewed Approve suggested edit on What is the greatest common divisor of $3^{3^{333}}+1$ and $3^{3^{334}}+1$?
1d
revised What is the greatest common divisor of $3^{3^{333}}+1$ and $3^{3^{334}}+1$?
added 26 characters in body; edited title
1d
comment Can you prove a definite integral has no closed form?
The short answer is no. At least not with currently available methods.
2d
comment How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$
Notice that $\ln2$ acts here like a regularized value of $\zeta(1)$.
2d
comment Calculus - Derivative help.
So, in your humble opinion, $\sqrt{a+b}=\sqrt a+\sqrt b$ ?
2d
revised Maximum area of a rectangular field that can be fenced and divided in half by a fence
deleted 2 characters in body
2d
answered Trying to solve a trig identity
2d
answered Maximum area of a rectangular field that can be fenced and divided in half by a fence
2d
answered The integral $\int_{\varepsilon}^1 r^n(1-r)^{k-n}\,dr $
2d
comment Why $1\frac{1}{2}\ne \frac{1}{2}$?
Why ? - To confuse people.
Aug
24
comment How does $2^n + 2^n = 2^{n+1}$?
Hint: $x+x=2x$, and $a^b\cdot a^c=a^{b+c}$.