Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0924)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=2

http://functions.wolfram.com/07.22.03.0924.01

Input Form

HypergeometricPFQ[{-(9/2)}, {2, 11/2}, -z] == (1/(523197480960 z^4)) (4 (2 z (-5157219375 - 3929310000 z - 4400827200 z^2 + 102662380800 z^3 + 110151489024 z^4 + 19004092416 z^5 + 923320320 z^6 + 14614528 z^7 + 65536 z^8) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-15471658125 - 9037413000 z - 11002068000 z^2 + 60710186880 z^3 + 101394459648 z^4 + 18554923008 z^5 + 916070400 z^6 + 14581760 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]]) + Pi (-15471658125 - 15913705500 z - 16974619200 z^2 - 52809926400 z^3 + 316859558400 z^4 + 422479411200 z^5 + 75107450880 z^6 + 3678732288 z^7 + 58392576 z^8 + 262144 z^9) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (-15471658125 - 15913705500 z - 16974619200 z^2 - 52809926400 z^3 + 316859558400 z^4 + 422479411200 z^5 + 75107450880 z^6 + 3678732288 z^7 + 58392576 z^8 + 262144 z^9) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML 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]