Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1393)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=3

http://functions.wolfram.com/07.25.03.1393.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {3, 11/2}, -z] == 42/(65 z^2) + (1/(3067084800 z^4)) ((42567525 - 174324150 z - 1010998800 z^2 + 643053600 z^3 + 1380376800 z^4 + 597823680 z^5 + 110565120 z^6 + 9902592 z^7 + 419072 z^8 + 6656 z^9)/E^z) + (1/(6134169600 z^(9/2))) (Sqrt[Pi] (-42567525 + 202702500 z - 1094593500 z^2 - 1945944000 z^3 + 2270268000 z^4 + 3269185920 z^5 + 1297296000 z^6 + 230630400 z^7 + 20217600 z^8 + 844800 z^9 + 13312 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]