/sci/ - Science & Math

>>8751034

[math] \dfrac{1}{1-q} = \sum_{k=0}^{\infty} q^k [/math]

eh?
Yes, I'm jelly.
You made me jelly. Mad jelly.
I'm gonna show you

[math] [n]_q := \sum_{k=0}^{n-1} q^k [/math]

[math] [n]_1 := \sum_{k=0}^{n-1} 1 = n [/math]

[math] \dfrac{1}{1-q} \int f(x) d_q x := x \sum_{k=0}^{\infty} q^k f(q^k x) [/math]

[math] \int x^m d_q x = \dfrac{x^{m+1}}{[m]_q} [/math]

[math] \left(\dfrac{d}{dx}\right)_q f(x) := \dfrac{f(qx)-f(x)}{qx-x} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, x^m = [m]_q\, x^{m-1} [/math]

[math] e_q(x) = \sum_{n=0}^\infty \dfrac{x^n}{[n]_q!} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, e_q(x) = e_q(x) [/math]

>>8751034

[math] \dfrac{1}{1-q} = \sum_{k=0}^{\infty} q^k [/math]

eh?
Yes, I'm jelly.
You made me jelly. Mad jelly.
I'm gonna show you

[math] [n]_q := \sum_{k=0}^{n-1} q^k [/math]

[math] [n]_1 := \sum_{k=0}^{n-1} 1 = n [/math]

[math] \dfrac{1}{1-q} \int f(x) d_q x := x \sum_{k=0}^{\infty} q^k f(q^k x) [/math]

[math] \int x^m d_q x = \dfrac{x^{m+1}}{[m+1]_q} [/math]

[math] \left(\dfrac{d}{dx}\right)_q f(x) := \dfrac{f(qx)-f(x)}{qx-x} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, x^m = [m]_q\, x^{m-1} [/math]

[math] e_q(z) = \sum_{n=0}^\infty \dfrac{z^n}{[n]_q!} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, e_q(z) = e_q(z) [/math]

>>8751034

[math] \dfrac{1}{1-q} = \sum_{k=0}^{\infty} q^k [/math]

eh?
Yes, I'm jelly.
You made me jelly. Mad jelly.
I'm gonna show you

[math] [n]_q := \sum_{k=0}^{n-1} q^k [/math]

[math] [n]_1 := \sum_{k=0}^{n-1} 1 = n [/math]

[math] \dfrac{1}{1-q} \int f(x) d_q x := x \sum_{k=0}^{\infty} q^k f(q^k x) [/math]

[math] \int x^m d_q x = \dfrac{x^{m+1}}{[m]_q} [/math]

[math] \left(\dfrac{d}{dx}\right)_q f(x) := \dfrac{f(qx)-f(x)}{qx-x} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, x^m = [m]_q\, x^{m-1} [/math]

[math] e_q(z) = \sum_{n=0}^\infty \dfrac{z^n}{[n]_q!} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, e_q(z) = e_q(z) [/math]

>>8751028

[math] \dfrac{1}{1-q} = \sum_{k=0}^{\infty} q^k [/math]

eh?
Yes, I'm jelly. You made me jelly. Mad jelly.
I'm gonna show you

[math] [n]_q := \sum_{k=0}^{n-1} q^k [/math]

[math] [n]_1 := \sum_{k=0}^{n-1} 1 = n [/math]

[math] \dfrac{1}{1-q} \int f(x) d_q x := x \sum_{k=0}^{\infty} q^k f(q^k x) [/math]

[math] \int x^m d_q x = \dfrac{x^{m+1}}{[m]_q} [/math]

[math] \left(\dfrac{d}{dx}\right)_q f(x) := \dfrac{f(qx)-f(x)}{qx-x} [/math]

[math] \left(\dfrac{d}{dx}\right)_q x^m = [m]_q x^{m-1} [/math]

[math] e_q(z) = \sum_{n=0}^\infty \dfrac{z^n}{[n]_q!} [/math]

[math] \left(\dfrac{d}{dx}\right)_q e_q(z) = e_q(z) [/math]