Formula engine

Formula guide

Memori turns plain text into proper maths, with no LaTeX, no backslashes and no dollar signs. Type a formula the natural way and it's formatted as you'd write it on paper, including the actuarial notation exams expect. Here's everything it understands, with what you type on the left and what shows on the right.

Two rules worth knowing. Anything longer than one character after a ^ or _ goes in braces, e.g. e^{kt}. And for an actuarial pre-subscript, type the underscore first, so _tp_x gives _tp_x, never t_px.

Try it

Type any formula below and it renders as you type, using the same engine as the app.

n∑i=1 x2i

Powers & subscripts

Use ^ for powers and _ for subscripts. Anything longer than one character goes in braces { }.

x^2

Power

e^{kt}

Multi-character power

ekt

x_i

Subscript

x_i

a_{ij}

Multi-character subscript

a_ij

x_i^2

Subscript and power together

x2i

e^{-x}

Negative power (braces)

e-x

Pre-subscripts (actuarial)

For a value that sits to the LEFT of the symbol, type the underscore first. Brace multiple characters together.

_tp_x

t-year survival probability

_tp_x

_nq_x

n-year mortality probability

_nq_x

_nE_x

Pure endowment

_nE_x

_{n|}q_x

Deferred mortality

_n|q_x

Accents (actuarial)

Wrap the content in parens. bar( ) is an overline (continuous), dot( ) and ddot( ) add one or two dots above, and angle( ) is the term symbol, usually written inside a subscript.

bar(A)_x

Continuous assurance

A_x

bar(a)_x

Continuous annuity

a_x

ddot(a)_x

Annuity-due

a_x

ddot(a)_{x:angle(n)}

Temporary annuity-due

a_x:n

a_{angle(n)}

Annuity-certain (term)

a_n

A_{x:angle(n)}

Endowment assurance

A_x:n

_{k|}^2bar(A)^1_{[x]:angle(n)}

All four corners at once, plus a bar accent, select bracket and the term symbol

2k|A1[x]:n

Fractions

Write (numerator)/(denominator) with balanced parens.

(a+b)/(c)

Fraction

a+bc

(dN)/(dt)

Derivative

dNdt

(d^2x)/(dt^2)

Second derivative

d2xdt2

(partial f)/(partial x)

Partial derivative

∂ f∂ x

(partial^2 f)/(partial x^2)

Second-order partial

∂2 f∂ x2

Sums, products & integrals

Add _ and ^ limits and they stack above and below the symbol.

sum_{i=1}^{n} i

Sum with limits

n∑i=1 i

int_0^1 x^2 dx

Definite integral

1∫0 x2 dx

prod_{k=1}^{n} k

Product

n∏k=1 k

sum_{n=1}^{infinity}

Infinite sum

∞∑n=1

Greek letters

Spell the name. Capitalise the first letter for the upper-case form.

alpha, beta, gamma

Lower case

α, β, γ

lambda, mu, sigma

Lower case

λ, μ, σ

Sigma, Omega, Delta

Upper case

Σ, Ω, Δ

Symbols & functions

sqrt(x)

Root

√(x)

sum, prod, int

∑ ∏ ∫

∑, ∏, ∫

partial, nabla

∂ ∇

∂, ∇

infinity, approx

∞ ≈

∞, ≈

Operators

>=, <=, !=

≥ ≤ ≠

≥, ≤, ≠

+-, ->, =>

± → ⇒

±, →, ⇒

a * b

Multiply (×)

a × b

Every Greek name works (alpha, beta, gamma … omega; capitalise for Γ Δ Σ Ω). In the app, the same reference is a tap away from the i button on any formula field.