Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8759)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8759.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 21/4}, -z] == ((2 Sqrt[z] (-8546860188942075 - 11942101193022000 z - 3252316920652800 z^2 + 1530875829288960 z^3 + 1440451227156480 z^4 - 557261996949504 z^5 + 2007915665817600 z^6 + 304090127007744 z^7 + 9470402887680 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (-14244766981570125 - 30033114064153200 z - 4336422560870400 z^2 - 2477955749068800 z^3 + 3481618999541760 z^4 - 1922292944732160 z^5 + 1755370179526656 z^6 + 295904993083392 z^7 + 9410273345536 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-42734300944710375 + 1067166489589200 z - 1393850108851200 z^2 - 1802149635686400 z^3 + 3119920591011840 z^4 - 1790752378060800 z^5 + 1788963333341184 z^6 + 297054970576896 z^7 + 9418863280128 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(3061751658577920 Sqrt[2] z^(15/4))

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]