Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0600)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=5/2

http://functions.wolfram.com/07.22.03.0600.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5/2, 6}, -z] == (1/(6159691137600 z^(9/2))) (4 (2 Sqrt[z] (-75442752000 - 41493513600 z - 50295168000 z^2 - 201180672000 z^3 + 1316662664625 z^4 + 1202463851400 z^5 + 200019666672 z^6 + 10582168320 z^7 + 212770560 z^8 + 1656832 z^9 + 4096 z^10) BesselJ[0, 2 Sqrt[z]] - (-150885504000 - 7544275200 z - 46523030400 z^2 - 342007142400 z^3 + 851805645075 z^4 + 1110829537440 z^5 + 194907457584 z^6 + 10477214208 z^7 + 211945728 z^8 + 1654784 z^9 + 4096 z^10) BesselJ[1, 2 Sqrt[z]]) + Pi z^(7/2) (-1361181746925 + 4234787657100 z + 4619768353200 z^2 + 789703992000 z^3 + 42117546240 z^4 + 849429504 z^5 + 6623232 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(7/2) (-1361181746925 + 4234787657100 z + 4619768353200 z^2 + 789703992000 z^3 + 42117546240 z^4 + 849429504 z^5 + 6623232 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]