4 Gamma function, a roadblock: $\int_0^\infty e^{-t}t^{x-1}\,dt = \frac{1}{x}\int_0^\infty e^{-u^{1/x}}\,du$? 1 Show for i' that ∀x x' + i' = x + i'' 0 A first order logic extended with binding terms like the familiar set descriptors $\{x:\varphi\}$ 0 Natural Deduction proof: C Ʌ D, C ↔ E |- (C V F) Ʌ (D V F) Ʌ (E V F) 0 Propositional Logic: $Τ\vDash\varphi\implies\existsΤ_0\subseteq T$ such that $Τ_0\vDash\varphi$

### Reputation (102)

 +2 If $f: \mathbb{N} \to \mathbb{N}$ is injective and $\lim a_n= a$, then $\lim a_{f(n)}= a$. +25 Show for i' that ∀x x' + i' = x + i'' +10 Understanding a proof that a collection of complex numbers on one side of a line through $0$ must have a non-zero sum +10 Gamma function, a roadblock: $\int_0^\infty e^{-t}t^{x-1}\,dt = \frac{1}{x}\int_0^\infty e^{-u^{1/x}}\,du$?

### Questions (4)

 2 Understanding a proof that a collection of complex numbers on one side of a line through $0$ must have a non-zero sum 2 Gamma function, a roadblock: $\int_0^\infty e^{-t}t^{x-1}\,dt = \frac{1}{x}\int_0^\infty e^{-u^{1/x}}\,du$? 0 Analyzing the sequence of functions: $\lim_{n\to\infty} \frac{(x-1)^n}{\ln(1+\frac 1n)5^{n+1}}$ 0 A simple Complex Function [Spivak 27-12(a)]

### Tags (11)

 4 calculus × 3 0 functional-analysis 4 gamma-function × 2 0 discrete-mathematics 1 logic × 4 0 propositional-calculus 0 complex-numbers × 4 0 proof-theory 0 geometry × 3 0 reference-request

### Account (1)

 Mathematics 102 rep 88 bronze badges