Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1685)

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=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=-3/2

http://functions.wolfram.com/07.25.03.1685.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {-(3/2), 6}, -z] == (180 (572 - 462 z + 133 z^2))/(4199 z^5) + (1/(264537 z^5)) ((4 (-1621620 - 311850 z + 121905 z^2 + 7560 z^3 - 37800 z^4 + 44352 z^5 - 62160 z^6 + 221952 z^7 + 146772 z^8 + 23504 z^9 + 1040 z^10))/E^z) + (8 Sqrt[Pi] (142443 z^(5/2) + 79002 z^(7/2) + 12012 z^(9/2) + 520 z^(11/2)) Erf[Sqrt[z]])/264537

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]