equation 5.3 eq:lin-binomial

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Supports

• depends_on lemma 7.60 Functional equation of the exponential ¶
  • depends_on proposition 7.68 The natural base ¶
    • depends_on remark 7.70 What the condition says ¶
  • depends_on proposition 7.61 The logarithm ¶
    • depends_on corollary 7.69 $\ee$ is the unique self-reproducing base ¶
      • depends_on remark 7.70 What the condition says ¶ ↺
    • depends_on definition 7.62 Real powers ¶
      • depends_on definition 7.90 The golden ratio ¶
        • depends_on proposition 7.91 The golden ratio ¶
      • depends_on proposition 7.63 Laws of real powers ¶
        • depends_on definition 7.90 The golden ratio ¶ ↺
        • depends_on lemma 7.67 The limit over real exponents ¶
        • depends_on proposition 7.68 The natural base ¶ ↺
        • depends_on proposition 7.91 The golden ratio ¶ ↺
        • depends_on proposition 7.89 Irrationality of square roots ¶
      • depends_on proposition 7.89 Irrationality of square roots ¶ ↺
    • depends_on lemma 7.67 The limit over real exponents ¶ ↺
    • depends_on proposition 7.68 The natural base ¶ ↺
    • depends_on proposition 7.63 Laws of real powers ¶ ↺
  • depends_on proposition 7.63 Laws of real powers ¶ ↺
• depends_on lemma 7.71 Derivatives; the Pythagorean identity ¶
  • depends_on lemma 7.75 The first quadrant ¶
    • depends_on proposition 7.76 $\pi$ as the circle constant ¶
    • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶
      • depends_on lemma 7.78 Chord, arc, tangent ¶
        • depends_on proposition 7.79 The polygon recursion ¶
      • depends_on proposition 7.85 Irrationality of $\pi$ ¶
        • depends_on remark 7.94 Three numbers, two kinds ¶
        • depends_on remark 7.87 Priority, and what irrationality does not give ¶
      • depends_on proposition 7.79 The polygon recursion ¶ ↺
      • depends_on proposition 7.83 Viète's product ¶
        • depends_on remark 7.84 One construction, two faces ¶
      • depends_on proposition 125.2 Crystallographic restriction ¶
        • depends_on remark 125.3 What the theorem does and does not forbid ¶
      • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶
    • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
  • depends_on lemma 7.78 Chord, arc, tangent ¶ ↺
  • depends_on lemma 9.136 Wallis integrals ¶
    • depends_on proposition 9.139 Series for the complete integral of the first kind ¶
      • depends_on proposition 9.144 The pendulum equation at finite amplitude ¶
  • depends_on proposition 7.76 $\pi$ as the circle constant ¶ ↺
  • depends_on proposition 7.85 Irrationality of $\pi$ ¶ ↺
  • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
  • depends_on proposition 9.141 First properties ¶
    • depends_on proposition 9.143 A cubic quadrature between two turning points ¶
    • depends_on proposition 9.142 The differential equation of the sine amplitude ¶
  • depends_on remark 7.80 Why these are the polygon perimeters ¶
• depends_on lemma 7.72 Addition theorems ¶
  • depends_on proposition 7.79 The polygon recursion ¶ ↺
  • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶ ↺
  • depends_on proposition 7.83 Viète's product ¶ ↺
  • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
  • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶ ↺
  • depends_on remark 7.80 Why these are the polygon perimeters ¶ ↺
• depends_on proposition 7.57 The limit definition ¶
  • depends_on lemma 7.67 The limit over real exponents ¶ ↺
  • depends_on remark 7.58 An identity, not a recipe ¶
    • depends_on remark 7.70 What the condition says ¶ ↺