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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), -(5/2)}, z] == (1/442047375) (442047375 + 884094750 z + 2554051500 z^2 + 25540515000 z^3 - 347351004000 z^4 + 2639867630400 z^5 - 36958146825600 z^6 - 208365815750400 z^7 - 320793877958400 z^8 - 227964126297600 z^9 - 89645181373440 z^10 - 21356249241600 z^11 - 3238870118400 z^12 - 320583997440 z^13 - 20824012800 z^14 - 874651392 z^15 - 22737408 z^16 - 330752 z^17 - 2048 z^18) - (1/442047375) (128 E^z Sqrt[Pi] (676889136000 z^(13/2) + 2436800889600 z^(15/2) + 3177397238400 z^(17/2) + 2070624124800 z^(19/2) + 773632490400 z^(21/2) + 178420611600 z^(23/2) + 26482385160 z^(25/2) + 2582700120 z^(27/2) + 166018545 z^(29/2) + 6920760 z^(31/2) + 178920 z^(33/2) + 2592 z^(35/2) + 16 z^(37/2)) 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]