Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an8c)

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=5, a₂>=5

For fixed z and a₁=5, a₂=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.an8c.01

Input Form

HypergeometricPFQ[{5, 5}, {-(7/2), 1}, -z] == (1/483840) (483840 + 3456000 z + 12441600 z^2 + 45158400 z^3 + 361267200 z^4 - 1011315231 z^5 + 811328250 z^6 - 295500180 z^7 + 56614104 z^8 - 6022352 z^9 + 354272 z^10 - 10688 z^11 + 128 z^12) + (1/967680) ((Sqrt[Pi] (-1329696225 z^(9/2) + 2637414000 z^(11/2) - 1873760400 z^(13/2) + 642384576 z^(15/2) - 118921824 z^(17/2) + 12388608 z^(19/2) - 719104 z^(21/2) + 21504 z^(23/2) - 256 z^(25/2)) Erfi[Sqrt[z]])/E^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]