Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2540)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=3

http://functions.wolfram.com/07.25.03.2540.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {3, 11/2}, -z] == (1/(3019898880 z^4)) ((-3274425 - 5301450 z - 19792080 z^2 + 137380320 z^3 + 1892455200 z^4 + 1995673920 z^5 + 710557440 z^6 + 107730432 z^7 + 7098112 z^8 + 165376 z^9)/E^z) + (1/(6039797760 z^(9/2))) (Sqrt[Pi] (3274425 + 3118500 z + 16839900 z^2 - 149688000 z^3 + 1222452000 z^4 + 5280992640 z^5 + 4610390400 z^6 + 1522160640 z^7 + 222393600 z^8 + 14361600 z^9 + 330752 z^10) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]